We address the general problem of random searches in the context of biological encounters.
We discuss deterministic and stochastic aspects of searching in general, focusing the destructive and nondestructive cases specifically. We review the empirical evidence supporting the LÚvy flight foraging hypothesis, as well as the more general possibility of superdiffusive foraging. We compare these hypotheses with competing and alternative theories of random searches. We explore the concepts of LÚvy walks as adaptive strategies and of superdiffusion as a critical survival state on the edge of extinction. We analyze LÚvy searches in other media and spaces, including lattices and newtorks as opposed to continuous environments. Finally, we explore several issues relevant to the practical application of these and related ideas of LÚvy and superdiffusive strategies to the general question of biological foraging.