Topological superconductors with Majorana fermion quasiparticles form a newly discovered class of matter. The Majorana fermion can be seen as half an electron, or more accurately, the electron wave function has split up into two separate parts. This non-local property is currently been intensively explored for implementing fault-tolerant quantum computation. In this talk I will first explain where and why Majorana fermions appear. I will then present some of our recent results in modeling topological superconductors with Majorana fermions. In particular I will focus on a simple mean to detect Majorana fermions, their robustness against disorder, and how they often appear in conjunction with spontaneous currents.