The aim of this talk will be to present results, many of them obtained jointly with A. Floer, on the existence and stability of standing and traveling wave solutions for nonlinear equations of Schrödinger and Klein-Gordon type. Emphasis will be placed on situations other than the flat, spatially homogeneous ones which have usually been studied in the past; in particular, equations with a potential or with spherical geometry will be considered. The relation between the hamiltonian structures for waves and particles will be discussed.