Very small systems--atomic and molecular clusters and nanoparticles--exhibit phase-like forms and, under suitable conditions, equilibria among these forms. However the phase behavior of such systems is very different from the familiar phase behavior of bulk matter. For example, instead of static coexistence along a single set of pressures and temperatures, the normal coexistence curve p(T), solid and liquid clusters may coexist in dynamic equilibrium along a band of temperatures and pressures. Moreover more than two phase-like forms of clusters may coexist. The transition from small-system behavior to bulk behavior gives new insights into the nature of first-order transitions. The nature of the small-system counterpart of a second-order transition is still an open question; the discussion will review what has been established thus far.