Data Templates
In Avalonia UI, data templates are not stored in the application resources. (The same is true of styles - see here.)
Instead, data templates are placed either inside a DataTemplates collection in a control, or inside the (and on Application):
For example, this code adds a data template to display the view model class MyViewModel:
<UserControl xmlns:viewmodels="using:MyApp.ViewModels"
x:DataType="viewmodels:ControlViewModel">
<UserControl.DataTemplates>
<DataTemplate DataType="viewmodels:FooViewModel">
<Border Background="Red" CornerRadius="8">
<TextBox Text="{Binding Name}"/>
</Border>
</DataTemplate>
</UserControl.DataTemplates>
<!-- Assuming that ControlViewModel.Foo is an object of type
MyApp.ViewModels.FooViewModel then a red border with a corner
radius of 8 containing a TextBox will be displayed here.
DataType is required only if you use Compiled Bindings, so it can be type-checked. -->
<ContentControl Content="{Binding Foo}"/>
<UserControl>
Data templates in Avalonia can also target interfaces and derived classes (which cannot be done in WPF) and so the order of DataTemplates can be important: DataTemplates within the same collection are evaluated in declaration order so you need to place them from most-specific to least-specific as you would in code.
Data Template Selector
In WPF you can create a DataTemplateSelector to select or create a DataTemplate based on the provided data. In Avalonia you cannot do this; but you can implement IDataTemplate which can be seen as a good replacement for the DataTemplateSelector. Please find a sample here.