Majorana fermions (particles which are their own antiparticle) may or may not exist in Nature as fundamental building blocks, but in the solid state they can be constructed out of electron and hole excitations. What is needed is a superconductor to hide the charge difference, and a topological phase to eliminate the zero-point motion that would cause an energy difference. A qubit encoded in a pair of Majorana fermions is expected to have an unusually long decoherence time. We will discuss strategies to detect Majorana fermions in a topological superconductor, as well as possible applications in a quantum computer.