  We provide a current perspective on the rapidly developing field of Majorana
zero modes in solid state systems. We emphasize the theoretical prediction,
experimental realization, and potential use of Majorana zero modes in future
information processing devices through braiding-based topological quantum
computation. Well-separated Majorana zero modes should manifest non-Abelian
braiding statistics suitable for unitary gate operations for topological
quantum computation. Recent experimental work, following earlier theoretical
predictions, has shown specific signatures consistent with the existence of
Majorana modes localized at the ends of semiconductor nanowires in the presence
of superconducting proximity effect. We discuss the experimental findings and
their theoretical analyses, and provide a perspective on the extent to which
the observations indicate the existence of anyonic Majorana zero modes in solid
state systems. We also discuss fractional quantum Hall systems (the 5/2 state)
in this context. We describe proposed schemes for carrying out braiding with
Majorana zero modes as well as the necessary steps for implementing topological
quantum computation.
