  In this review, we present the encounter-based approach to target search
problems, in which the diffusive dynamics is described by the joint probability
of the position of the particle and the number of its encounters with a given
target set. The knowledge of the statistics of encounters allows one to
implement various mechanisms of reactions on the target set, beyond
conventional reaction schemes. We formulate this approach for three relevant
settings: discrete random walks, Brownian motion with bulk reactions, and
reflected Brownian motion with surface reactions. In all cases, we discuss the
advantages of this approach, its recent applications and possible extensions.
