Encounter-based methods provide a general probabilistic framework for modelling adsorption on the surface or interior of a target. An adsorption event occurs when the contact time with the target exceeds a random threshold. If the probability distribution of the latter is an exponential function, then one recovers the Markovian example of adsorption at a constant rate, whereas a non-exponential distribution signifies non-Markovian adsorption. In the case of a partially adsorbing target surface (interior) the contact time is given by a Brownian functional known as the boundary local time (occupation time). In this talk we provide an overview of encounter-based methods. We begin by considering simple diffusive search processes. We then present several extensions of the theory such as search processes with stochastic resetting, active run-and-tumble particles, and diffusion across semipermeable membranes. Various applications to cell biology are also described.