OsmSharp is an open-source mapping tool designed to work with OpenStreetMap. Most important features are offline rendering of vector-data and routing. All OsmSharp features are available on Android, iOS, Windows Phone (using the Xamarin products) and the regulars Linux, Windows, OSX (using Mono).
Rendering OpenStreetMap-data using MapCSS or a custom style interpreter. Using a vector format for mobile devices rendering offline map data on Android/iOS is also possible.
Routing also using OpenStreetMap-data or most other available networks. Custom routing profiles are possible and offline routing on mobile devices can be done using a pre-processed binary format.
OsmSharp started as a project for logistical optimisation. There are several solvers for the (A)TSP and some VRP's.
OpenStreetMap data can be hard to handle sometimes. Basic filtering, conversion and database providers exists to import/export OpenStreetMap data.