Consider a particle diffusing in space, which occasionally jumps at random
times to new regions of space or even to its initial location. The dynamics
provides a simple realization of intermittent search processes, with
diffusion mimicking the foraging process in which a target is looked for, and
resetting implementing the process of relocation. We will discuss recent
advances in characterizing the long-time properties of such a dynamics in an
assembly of independent particles as well as in systems with strong
interaction between the constituents.