  Among the major approaches that are being pursued for realizing quantum bits,
the Majorana-based platform has been the most recent to be launched. It
attempts to realize qubits which store quantum information in a
topologically-protected manner. The quantum information is protected by its
nonlocal storage in localized and well-separated Majorana zero modes, and
manipulated by exploiting their nonabelian quantum exchange properties.
Realizing these topological qubits is experimentally challenging, requiring
superconductivity, helical electrons (created by spin-orbit coupling) and
breaking of time reversal symmetry to all cooperate in an uncomfortable
alliance. Over the past decade, several candidate material systems for
realizing Majorana-based topological qubits have been explored, and there is
accumulating, though still debated, evidence that zero modes are indeed being
realized. This paper reviews the basic physical principles on which these
approaches are based, the material systems that are being developed, and the
current state of the field. We highlight both the progress made and the
challenges that still need to be overcome.
