  When an interacting many-body system, such as a magnet, is driven in time by
an external perturbation, such as a magnetic field,the system cannot respond
instantaneously due to relaxational delay. The response of such a system under
a time-dependent field leads to many novel physical phenomena with intriguing
physics and important technological applications. For oscillating fields, one
obtains hysteresis that would not occur under quasistatic conditions in the
presence of thermal fluctuations. Under some extreme conditions of the driving
field, one can also obtain a non-zero average value of the variable undergoing
such dynamic hysteresis. This non-zero value indicates a breaking of symmetry
of the hysteresis loop, around the origin. Such a transition to the
spontaneously broken symmetric phase occurs dynamically when the driving
frequency of the field increases beyond its threshold value which depends on
the field amplitude and the temperature. Similar dynamic transitions also occur
for pulsed and stochastically varying fields. We present an overview of the
ongoing researches in this not-so-old field of dynamic hysteresis and
transitions.
