  We present a pedagogical review of topological superconductivity and its
consequences in spin-orbit coupled semiconductor/superconductor
heterostructures. We start by reviewing the historical origins of the notions
of Dirac and Majorana fermions in particle physics and discuss how lower
dimensional versions of these emerge in one dimensional superconductors.
Ultimately, we focus on Majorana zero-modes, which emerge at defects in the
Majorana equation. We then review the definition of the topological invariant,
and how it allows the prediction of such Majorana modes from the bulk
bandstructure of realistic superconductors, which do not have Lorentz
invariance. Finally, we end with a discussion of protocols for how to detect
such Majorana modes and use them for topological quantum computation.

Superconductivity