  In this review, after providing the basic physical concept behind quantum
annealing (or adiabatic quantum computation), we present an overview of some
recent theoretical as well as experimental developments pointing to the issues
which are still debated. With a brief discussion on the fundamental ideas of
continuous and discontinuous quantum phase transitions, we discuss the
Kibble-Zurek scaling of defect generation following a ramping of a quantum many
body system across a quantum critical point. In the process, we discuss
associated models, both pure and disordered, and shed light on implementations
and some recent applications of the quantum annealing protocols. Furthermore,
we discuss the effect of environmental coupling on quantum annealing. Some
possible ways to speed up the annealing protocol in closed systems are
elaborated upon: We especially focus on the recipes to avoid discontinuous
quantum phase transitions occurring in some models where energy gaps vanish
exponentially with the system size.
