  Agents searching for a target can improve their efficiency by memorizing
where they have already been searching or by cooperating with other searchers
and using strategies that benefit from collective effects. This chapter reviews
such concepts: non-Markovian and collective search strategies. We start with
the first passage properties of continuous non-Markovian processes and then
proceed to the discrete random walker with 1-step and n-step memory. Next we
discuss the auto-chemotactic walker, a random walker that produces a diffusive
chemotactic cue from which the walker tries to avoid. Then ensembles of agents
searching for a single target are discussed, whence the search efficiency may
comprise in addition to the first passage time also metabolic costs. We
consider the first passage properties of ensembles of chemotactic random
walkers and then the pursuit problem, in which searchers (or hunters /
predators) see the mobile target over a certain distance. Evasion strategies of
single or many targets are also elucidated. Finally we review collective
foraging strategies comprising many searchers and many immobile targets. We
finish with an outlook on future research directions comprising yet unexplored
search strategies of immune cells and in swarm robotics.
