How to handle WndProc messages in WPF?

You can do this via the System.Windows.Interop namespace which contains a class named HwndSource.

Example of using this

using System;
using System.Windows;
using System.Windows.Interop;

namespace WpfApplication1
{
    public partial class Window1 : Window
    {
        public Window1()
        {
            InitializeComponent();
        }

        protected override void OnSourceInitialized(EventArgs e)
        {
            base.OnSourceInitialized(e);
            HwndSource source = PresentationSource.FromVisual(this) as HwndSource;
            source.AddHook(WndProc);
        }

        private IntPtr WndProc(IntPtr hwnd, int msg, IntPtr wParam, IntPtr lParam, ref bool handled)
        {
            // Handle messages...

            return IntPtr.Zero;
        }
    }
}

Completely taken from the excellent blog post: Using a custom WndProc in WPF apps by Steve Rands

Actually, as far as I understand such a thing is indeed possible in WPF using HwndSource and HwndSourceHook. See this thread on MSDN as an example. (Relevant code included below)

// 'this' is a Window
HwndSource source = HwndSource.FromHwnd(new WindowInteropHelper(this).Handle);
source.AddHook(new HwndSourceHook(WndProc));

private static IntPtr WndProc(IntPtr hwnd, int msg, IntPtr wParam, IntPtr lParam, ref bool handled)
{
    //  do stuff

    return IntPtr.Zero;
}

Now, I'm not quite sure why you'd want to handle Windows Messaging messages in a WPF application (unless it's the most obvious form of interop for working with another WinForms app). The design ideology and the nature of the API is very different in WPF from WinForms, so I would suggest you just familiarise yourself with WPF more to see exactly why there is no equivalent of WndProc.