An overview is presented on interdisciplinary studies into complexity of wave processes with the main attention to wave–wave, field–field, wave–internal structure a.o. interactions. The nonlinearity of these processes creates specific physical phenomena as a result of interactions. The basic assumptions of modelling, main hypotheses adopted and resulting governing equations are presented. Due to complexity of processes, numerical methods are mainly used for the analysis. However, in many cases the methods (the finite volume method, the pseudospectral method) must be modified in order to guarantee the accuracy and stability of solutions. The spectrum of problems modelled and analysed is wide including dynamical processes in solids, fluids and tissues.
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