If you go to a website from a mobile device, you will notice the website is redirected to a subdomain stars with m.website.com. This is mobile optimized website.
You can build mobile optimized websites using ASP.NET and other technologies. All you need to know is, what content you want to show that will fit on a mobile device.
This white paper talks about how to architect and build a mobile enabled website using ASP.NET.
ASP.NET 3.5 included ASP.NET Mobile Controls: a set of server controls for mobile devices in the System.Web.Mobile.dll assembly and the System.Web.UI.MobileControls namespace. The assembly is still included in ASP.NET 4, but it is deprecated. Developers are advised to migrate to more modern approaches, such as those described in this paper.
The reason why ASP.NET Mobile Controls have been marked as obsolete is that their design is oriented around the mobile phones that were common around 2005 and earlier. The controls are mainly designed to render WML or cHTML markup (instead of regular HTML) for the WAP browsers of that era. But WAP, WML, and cHTML are no longer relevant for most projects, because HTML has now become the ubiquitous markup language for mobile and desktop browsers alike.