diff --git a/src/Linq2GraphQL.Client/Exceptions/GraphQueryTranslationException.cs b/src/Linq2GraphQL.Client/Exceptions/GraphQueryTranslationException.cs
new file mode 100644
index 00000000..aaf409f7
--- /dev/null
+++ b/src/Linq2GraphQL.Client/Exceptions/GraphQueryTranslationException.cs
@@ -0,0 +1,35 @@
+using System.Linq.Expressions;
+
+namespace Linq2GraphQL.Client;
+
+/// <summary>
+///     Thrown when an expression passed to <c>Include</c> or <c>Select</c> cannot be turned into a GraphQL
+///     selection, either because it uses a construct that has no GraphQL equivalent or because it reads
+///     something that is not part of the query.
+/// </summary>
+/// <remarks>
+///     The query text does not exist yet when translation fails, so unlike
+///     <see cref="GraphQueryRequestException" /> and <see cref="GraphQueryExecutionException" /> this
+///     exception carries the offending <see cref="Expression" /> instead.
+///     It derives from <see cref="NotSupportedException" />, which is what the parser threw before this type
+///     existed, so callers that catch that keep working.
+/// </remarks>
+public class GraphQueryTranslationException : NotSupportedException
+{
+    public GraphQueryTranslationException(string message, Expression expression, string memberName = null)
+        : base(message)
+    {
+        Expression = expression;
+        MemberName = memberName;
+    }
+
+    /// <summary>
+    ///     The part of the expression that could not be translated.
+    /// </summary>
+    public Expression Expression { get; }
+
+    /// <summary>
+    ///     The LINQ operator or GraphQL member the failure is about, when it is about a single one.
+    /// </summary>
+    public string MemberName { get; }
+}
diff --git a/src/Linq2GraphQL.Client/Visitors/LinqOperator.cs b/src/Linq2GraphQL.Client/Visitors/LinqOperator.cs
index 5bedfbfc..22879a3a 100644
--- a/src/Linq2GraphQL.Client/Visitors/LinqOperator.cs
+++ b/src/Linq2GraphQL.Client/Visitors/LinqOperator.cs
@@ -15,15 +15,18 @@ internal enum LinqOperatorKind
     Projection,
 
     /// <summary>
-    ///     The operator keeps the source element type, or reduces the sequence to one of its elements or to a
-    ///     scalar computed from them (<c>Where</c>, <c>OrderBy</c>, <c>First</c>, <c>Count</c>, ...).
+    ///     The operator keeps the source element type, or reduces the sequence to one of its elements, to a
+    ///     scalar computed from them, or to another container holding them (<c>Where</c>, <c>OrderBy</c>,
+    ///     <c>First</c>, <c>Count</c>, <c>ToDictionary</c>, <c>GroupBy</c>, ...).
     ///     The selection stays on the source node; any lambda is a client side predicate or key selector whose
     ///     members still have to be fetched for it to work.
     /// </summary>
     PassThrough,
 
     /// <summary>
-    ///     A known LINQ operator that cannot be translated, typically because it combines several sequences.
+    ///     A known LINQ operator that cannot be translated, because it combines several sequences
+    ///     (<c>Concat</c>, <c>Join</c>, <c>Zip</c>, ...) or folds the elements into an accumulator that the
+    ///     selection cannot follow (<c>Aggregate</c>).
     /// </summary>
     Unsupported
 }
@@ -40,12 +43,15 @@ internal static class LinqOperator
     [
         "All",
         "Any",
+        "Append",
         "AsEnumerable",
         "AsQueryable",
         "Average",
         "Cast",
         "Chunk",
+        "Contains",
         "Count",
+        "CountBy",
         "DefaultIfEmpty",
         "Distinct",
         "DistinctBy",
@@ -53,6 +59,8 @@ internal static class LinqOperator
         "ElementAtOrDefault",
         "First",
         "FirstOrDefault",
+        "GroupBy",
+        "Index",
         "Last",
         "LastOrDefault",
         "LongCount",
@@ -65,7 +73,9 @@ internal static class LinqOperator
         "OrderBy",
         "OrderByDescending",
         "OrderDescending",
+        "Prepend",
         "Reverse",
+        "Shuffle",
         "Single",
         "SingleOrDefault",
         "Skip",
@@ -78,8 +88,11 @@ internal static class LinqOperator
         "ThenBy",
         "ThenByDescending",
         "ToArray",
+        "ToDictionary",
         "ToHashSet",
         "ToList",
+        "ToLookup",
+        "TryGetNonEnumeratedCount",
         "Where"
     ];
 
diff --git a/src/Linq2GraphQL.Client/Visitors/QueryExpressionVisitor.cs b/src/Linq2GraphQL.Client/Visitors/QueryExpressionVisitor.cs
index ef1c1bf9..08094570 100644
--- a/src/Linq2GraphQL.Client/Visitors/QueryExpressionVisitor.cs
+++ b/src/Linq2GraphQL.Client/Visitors/QueryExpressionVisitor.cs
@@ -131,7 +131,11 @@ private QueryNode ResolveCall(MethodCallExpression call)
 
             case LinqOperatorKind.Unsupported:
                 throw Unsupported(call,
-                    $"the LINQ operator '{call.Method.Name}' cannot be translated to a GraphQL selection");
+                    $"the LINQ operator '{call.Method.Name}' has no GraphQL equivalent and the selection cannot " +
+                    "follow what it returns",
+                    $"Select the fields the query needs and call '{call.Method.Name}' on the result of " +
+                    "ExecuteAsync instead.",
+                    call.Method.Name);
 
             default:
                 // An ordinary method such as string.ToUpper(). It selects nothing itself, but its target and
@@ -155,7 +159,8 @@ private QueryNode ResolveGraphMethod(MethodCallExpression call)
         if (parent == null)
         {
             throw Unsupported(call,
-                $"the target of '{call.Method.Name}' is not part of the query");
+                $"the target of '{call.Method.Name}' is not part of the query",
+                memberName: call.Method.Name);
         }
 
         return parent.AddChildNode(new QueryNode(call.Method, arguments: GetArguments(call)));
@@ -181,9 +186,21 @@ private QueryNode ResolveLinqOperator(MethodCallExpression call, LinqOperatorKin
         {
             // Predicates and key selectors run on the client, so the members they touch must be fetched, but
             // the selection itself stays on the sequence.
+            var elementType = GetElementType(call.Arguments[0].Type);
+
             foreach (var lambda in lambdas)
             {
                 Bind(lambda.Parameters[0], source);
+
+                // GroupBy's result selector takes (key, elements): the elements are the sequence itself.
+                for (var i = 1; i < lambda.Parameters.Count; i++)
+                {
+                    if (elementType != null && GetElementType(lambda.Parameters[i].Type) == elementType)
+                    {
+                        Bind(lambda.Parameters[i], source);
+                    }
+                }
+
                 Select(lambda.Body);
             }
 
@@ -217,6 +234,21 @@ private QueryNode ResolveLinqOperator(MethodCallExpression call, LinqOperatorKin
         return projected;
     }
 
+    /// <summary>
+    ///     The element type of a sequence type, or null when the type is not a sequence.
+    /// </summary>
+    private static Type GetElementType(Type type)
+    {
+        if (type.IsGenericType && type.GetGenericTypeDefinition() == typeof(IEnumerable<>))
+        {
+            return type.GetGenericArguments()[0];
+        }
+
+        return type.GetInterfaces()
+            .FirstOrDefault(e => e.IsGenericType && e.GetGenericTypeDefinition() == typeof(IEnumerable<>))
+            ?.GetGenericArguments()[0];
+    }
+
     private static List<LambdaExpression> GetLambdas(MethodCallExpression call)
     {
         var lambdas = new List<LambdaExpression>();
@@ -298,9 +330,10 @@ private QueryNode Scope(ParameterExpression parameter)
             return node;
         }
 
-        throw new NotSupportedException(
+        throw new GraphQueryTranslationException(
             $"Cannot translate '{parameter.Name}' of type '{parameter.Type.Name}': it is not bound to a field of " +
-            "the query. Only the parameters of the lambdas passed to Include and Select can be used to select fields.");
+            "the query. Only the parameters of the lambdas passed to Include and Select can be used to select fields.",
+            parameter);
     }
 
     private static Expression Unwrap(Expression expression)
@@ -325,8 +358,12 @@ private static Expression Unwrap(Expression expression)
         return null;
     }
 
-    private static NotSupportedException Unsupported(Expression expression, string reason)
+    private static GraphQueryTranslationException Unsupported(Expression expression, string reason,
+        string hint = null, string memberName = null)
     {
-        return new NotSupportedException($"Cannot translate '{expression}' into a GraphQL selection: {reason}.");
+        var message = $"Cannot translate '{expression}' into a GraphQL selection: {reason}.";
+
+        return new GraphQueryTranslationException(hint == null ? message : message + " " + hint, expression,
+            memberName);
     }
 }
diff --git a/test/Linq2GraphQL.Tests/ExpressionParserTests.cs b/test/Linq2GraphQL.Tests/ExpressionParserTests.cs
index 08ef9cfb..7b532695 100644
--- a/test/Linq2GraphQL.Tests/ExpressionParserTests.cs
+++ b/test/Linq2GraphQL.Tests/ExpressionParserTests.cs
@@ -282,13 +282,67 @@ public void CapturedValue_SelectsNothing()
         ShouldSelect((OrdersConnection e) => new { e.TotalCount, Captured = captured.OrderId }, "totalCount*");
     }
 
+    [Fact]
+    public void MaterialisingOperator_FetchesWhatItReads()
+    {
+        ShouldSelect((OrdersConnection e) => e.Nodes.ToDictionary(n => n.OrderId, n => n.Customer),
+            """
+            nodes*
+            nodes.orderId*
+            nodes.customer*
+            """);
+    }
+
+    [Fact]
+    public void MaterialisingOperator_WithComparer_FetchesWhatItReads()
+    {
+        ShouldSelect(
+            (OrdersConnection e) => e.Nodes.ToDictionary(n => n.Customer.CustomerName, n => n,
+                StringComparer.OrdinalIgnoreCase),
+            """
+            nodes*
+            nodes.customer
+            nodes.customer.customerName*
+            """);
+    }
+
+    [Fact]
+    public void GroupBy_FetchesTheKeyFields()
+    {
+        ShouldSelect((OrdersConnection e) => e.Nodes.GroupBy(n => n.OrderId),
+            """
+            nodes*
+            nodes.orderId*
+            """);
+    }
+
+    [Fact]
+    public void GroupBy_WithResultSelector_BindsTheElements()
+    {
+        ShouldSelect(
+            (OrdersConnection e) => e.Nodes.GroupBy(n => n.Customer.CustomerName,
+                (name, orders) => orders.Select(o => o.OrderId)),
+            """
+            nodes*
+            nodes.customer
+            nodes.customer.customerName*
+            nodes.orderId*
+            """);
+    }
+
     [Fact]
     public void UnsupportedOperator_IsReported()
     {
-        var exception = Should.Throw<NotSupportedException>(() =>
-            Parse((OrdersConnection e) => e.Nodes.GroupBy(n => n.OrderId)));
+        var exception = Should.Throw<GraphQueryTranslationException>(() =>
+            Parse((OrdersConnection e) => e.Nodes.Concat(e.Nodes)));
+
+        exception.Message.ShouldContain("Concat");
+        exception.Message.ShouldContain("ExecuteAsync");
+        exception.MemberName.ShouldBe("Concat");
+        exception.Expression.ShouldNotBeNull();
 
-        exception.Message.ShouldContain("GroupBy");
+        // The parser threw NotSupportedException before the exception got a name of its own.
+        exception.ShouldBeAssignableTo<NotSupportedException>();
     }
 
     [Fact]
@@ -302,8 +356,9 @@ public void UnboundParameter_IsReported()
 
         var root = new QueryNode(typeof(OrdersConnection), "root", null, null, true);
 
-        var exception = Should.Throw<NotSupportedException>(() => Utilities.ParseExpression(lambda, root));
+        var exception = Should.Throw<GraphQueryTranslationException>(() => Utilities.ParseExpression(lambda, root));
         exception.Message.ShouldContain("stray");
+        exception.Expression.ShouldBe(stray);
     }
 }
 
diff --git a/test/Linq2GraphQL.Tests/QueryOperatorTests.cs b/test/Linq2GraphQL.Tests/QueryOperatorTests.cs
index 4d36d8e6..594acdcb 100644
--- a/test/Linq2GraphQL.Tests/QueryOperatorTests.cs
+++ b/test/Linq2GraphQL.Tests/QueryOperatorTests.cs
@@ -1,3 +1,4 @@
+using Linq2GraphQL.Client;
 using Linq2GraphQL.TestClient;
 using Shouldly;
 
@@ -115,14 +116,53 @@ public async Task SelectMany_WithResultSelector()
         result.ShouldAllBe(e => e.CustomerName != null && e.OrderId != Guid.Empty);
     }
 
+    [Fact]
+    public async Task ToDictionary_FetchesTheKeyAndElementFields()
+    {
+        var query = sampleClient
+            .Query
+            .Orders()
+            .Select(e => e.Nodes.ToDictionary(n => n.OrderId.ToString(), n => n.Customer.CustomerName,
+                StringComparer.OrdinalIgnoreCase));
+
+        var request = await query.GetRequestAsync();
+        request.Query.ShouldContain("customerName");
+        request.Query.ShouldContain("orderId");
+
+        var result = await query.ExecuteAsync();
+
+        result.ShouldNotBeEmpty();
+        result.Values.ShouldAllBe(e => e != null);
+    }
+
+    [Fact]
+    public async Task GroupBy_FetchesTheKeyFields()
+    {
+        var query = sampleClient
+            .Query
+            .Orders()
+            .Select(e => e.Nodes
+                .GroupBy(n => n.Customer.CustomerName, (name, orders) => orders.Select(o => o.OrderId)));
+
+        var request = await query.GetRequestAsync();
+        request.Query.ShouldContain("customerName");
+
+        var result = (await query.ExecuteAsync()).ToList();
+
+        result.ShouldNotBeEmpty();
+        result.SelectMany(e => e).ShouldAllBe(e => e != Guid.Empty);
+    }
+
     [Fact]
     public async Task UnsupportedOperator_IsReported()
     {
-        var exception = Should.Throw<NotSupportedException>(() => sampleClient
+        var exception = Should.Throw<GraphQueryTranslationException>(() => sampleClient
             .Query
             .Orders()
-            .Select(e => e.Nodes.GroupBy(n => n.OrderId)));
+            .Select(e => e.Nodes.Concat(e.Nodes)));
 
-        exception.Message.ShouldContain("GroupBy");
+        exception.Message.ShouldContain("Concat");
+        exception.Message.ShouldContain("ExecuteAsync");
+        exception.MemberName.ShouldBe("Concat");
     }
 }