  Active particles, which are self-propelled nonequilibrium systems, are
modelled by overdamped Langevin equations with colored noise, emulating the
self-propulsion. In this chapter, we present a review of the theoretical
results for the target search problem of these particles. We focus on three
most well-known models, namely, run-and-tumble particles, active Brownian
particles, and direction reversing active Brownian particles, which differ in
their self-propulsion dynamics. For each of these models, we discuss the
first-passage and survival probabilities in the presence of an absorbing
target. We also discuss how resetting helps the active particles find targets
in a finite time.
