This report gives an overview of the field of nonlinear dynamical systems (NDS) from an FOI perspective. The overview is commenced with some general observations about mathematical modeling and a short recapitulation of the differences between linear and nonlinear dynamics. After this, a few aspects on various application areas of NDS that are represented within FOI are given followed by an historical retrospective and a somewhat deeper survey of the NDS field. Part of the report treats some examples of the use of NDS methods which illustrate the advantages for FOI that can be achieved by connection of theory for NDS with knowledge from one or several application areas in order to obtain synergy effects. Particular emphasis is put on application areas where FOI has existing competence groups and where further effors can give good return on investment for FOI and the Swedish Armed Forces/Swedish Defence Material Administration. Here, return on investment is to be interpreted as research for which the applications are of direct interest to the Swedish Armed Forces or swedish industry, or research collaboration which can provide this in a near future. Finally, a few general remarks and conclusions of the work are given.