  Shortcuts to adiabaticity guide given systems to final destinations of
adiabatic control via fast tracks. Various methods were proposed as varieties
of shortcuts to adiabaticity. Basic theory of shortcuts to adiabaticity was
established in the 2010s, but it has still been developing and many fundamental
findings have been reported. In this Topical Review, we give a pedagogical
introduction to theory of shortcuts to adiabaticity and revisit relations
between different methods. Some versatile approximations in counterdiabatic
driving, which is one of the methods of shortcuts to adiabaticity, will be
explained in detail. We also summarize recent progress in studies of shortcuts
to adiabaticity.
