I have a DataGrid simplified looking like this:
<DataGrid AutoGenerateColumns="False" 
          ItemsSource="{Binding Parts}" 
          SelectedItem="{Binding SelectedPart}" >
    <DataGrid.Columns>
        <DataGridTextColumn Header="Name" Binding="{Binding Path=Name, Mode=TwoWay}" />
        <DataGridTemplateColumn Header="PartType" >
            <DataGridTemplateColumn.CellEditingTemplate>
                <DataTemplate>
                    <ComboBox ItemsSource="{Binding RelativeSource={RelativeSource AncestorType={x:Type DataGrid}}, Path=DataContext.PartTypes}" 
                              SelectedItem="{Binding PartType, Mode=TwoWay, UpdateSourceTrigger=LostFocus}" />
                </DataTemplate>
            </DataGridTemplateColumn.CellEditingTemplate>
            <DataGridTemplateColumn.CellTemplate>
                <DataTemplate>
                    <TextBlock Text="{Binding PartType}" />
                </DataTemplate>
            </DataGridTemplateColumn.CellTemplate>
        </DataGridTemplateColumn>
    </DataGrid.Columns>
</DataGrid>
My ViewModel looks something like this:
public class PartListViewModel
{
    private ObservableCollection<Part> _parts;
    public ObservableCollection<Part> Parts
    {
        get { return _parts; }
        set
        {
            _parts = value;
             OnPropertyChanged("Parts");
        }
    }
    private Part _selectedPart;
    public Part SelectedPart
    {
        get { return _selectedPart; }
        set
        {
            _selectedPart = value;
            OnPropertyChanged("SelectedPart");
        }
    }
}
Now I want changes to datagrid cells being stored immediately to the database. How to do that in MVVM?
Currently I listen to the OnCellEditEnding event of the DataGrid and save the record in the code-behind. But that is pretty ugly:
private void DataGrid_OnCellEditEnding(object sender, DataGridCellEditEndingEventArgs e)
{
    var viewModel = (PartListViewModel) DataContext;
    viewModel.SavePart((Part) e.Row.Item);
}