How to refresh an AlertDialog in Flutter?

Use StatefulBuilder to use setState inside Dialog and update Widgets only inside of it.

showDialog(
  context: context,
  builder: (context) {
    String contentText = "Content of Dialog";
    return StatefulBuilder(
      builder: (context, setState) {
        return AlertDialog(
          title: Text("Title of Dialog"),
          content: Text(contentText),
          actions: <Widget>[
            TextButton(
              onPressed: () => Navigator.pop(context),
              child: Text("Cancel"),
            ),
            TextButton(
              onPressed: () {
                setState(() {
                  contentText = "Changed Content of Dialog";
                });
              },
              child: Text("Change"),
            ),
          ],
        );
      },
    );
  },
);

This is because you need to put your AlertDialog in its own StatefulWidget and move all state manipulation logic on the color there.

Update:

void main() => runApp(MaterialApp(home: Home()));

class Home extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
        body: Center(
            child: RaisedButton(
      child: Text('Open Dialog'),
      onPressed: () {
        showDialog(
            context: context,
            builder: (_) {
              return MyDialog();
            });
      },
    )));
  }
}

class MyDialog extends StatefulWidget {
  @override
  _MyDialogState createState() => new _MyDialogState();
}

class _MyDialogState extends State<MyDialog> {
  Color _c = Colors.redAccent;
  @override
  Widget build(BuildContext context) {
    return AlertDialog(
      content: Container(
        color: _c,
        height: 20.0,
        width: 20.0,
      ),
      actions: <Widget>[
        FlatButton(
            child: Text('Switch'),
            onPressed: () => setState(() {
                  _c == Colors.redAccent
                      ? _c = Colors.blueAccent
                      : _c = Colors.redAccent;
                }))
      ],
    );
  }
}

Use a StatefulBuilder in the content section of the AlertDialog. Even the StatefulBuilder docs actually have an example with a dialog.

What it does is provide you with a new context, and setState function to rebuild when needed.

The sample code:

showDialog(
  context: context,
  builder: (BuildContext context) {

    int selectedRadio = 0; // Declare your variable outside the builder
    
    return AlertDialog( 
      content: StatefulBuilder(  // You need this, notice the parameters below:
        builder: (BuildContext context, StateSetter setState) {
          return Column(  // Then, the content of your dialog.
            mainAxisSize: MainAxisSize.min,
            children: List<Widget>.generate(4, (int index) {
              return Radio<int>(
                value: index,
                groupValue: selectedRadio,
                onChanged: (int value) {
                  // Whenever you need, call setState on your variable
                  setState(() => selectedRadio = value);
                },
              );
            }),
          );
        },
      ),
    );
  },
);

And as I mentioned, this is what is said on the showDialog docs:

[...] The widget returned by the builder does not share a context with the location that showDialog is originally called from. Use a StatefulBuilder or a custom StatefulWidget if the dialog needs to update dynamically.

First you need to use StatefulBuilder. Then i am setting _setState variable, which even could be used outside StatefulBuilder, to set new state.

StateSetter _setState;
String _demoText = "test";

showDialog(
  context: context,
  builder: (BuildContext context) {

    return AlertDialog( 
      content: StatefulBuilder(  // You need this, notice the parameters below:
        builder: (BuildContext context, StateSetter setState) {
          _setState = setState;
          return Text(_demoText);
        },
      ),
    );
  },
);

_setState is used same way as setState method. For example like this:

_setState(() {
    _demoText = "new test text";
});

If you're separating your data from the UI via View Models and using the Provider package with ChangeNotifier, you'll need to include your current model like so within the widget calling the dialog:

showDialog(context: context, builder: (dialog) {
              return ChangeNotifierProvider.value(
                  value: context.read<ViewModel>(),
                child: CustomStatefulDialogWidget(),
              );
            },

Note that there may be a cleaner way to do this but this worked for me.

Additional info regarding Provider: https://flutter.dev/docs/development/data-and-backend/state-mgmt/simple