  In this Topical Review we consider stochastic processes under resetting,
which have attracted a lot of attention in recent years. We begin with the
simple example of a diffusive particle whose position is reset randomly in time
with a constant rate $r$, which corresponds to Poissonian resetting, to some
fixed point (e.g. its initial position). This simple system already exhibits
the main features of interest induced by resetting: (i) the system reaches a
nontrivial nonequilibrium stationary state (ii) the mean time for the particle
to reach a target is finite and has a minimum, optimal, value as a function of
the resetting rate $r$. We then generalise to an arbitrary stochastic process
(e.g. L\'evy flights or fractional Brownian motion) and non-Poissonian
resetting (e.g. power-law waiting time distribution for intervals between
resetting events). We go on to discuss multiparticle systems as well as
extended systems, such as fluctuating interfaces, under resetting. We also
consider resetting with memory which implies resetting the process to some
randomly selected previous time. Finally we give an overview of recent
developments and applications in the field.
