ABSTRACT Geophysical phenomena are often characterized by complex, random looking deviations of the relevant variables from their average values. Traditional approaches attribute this complexity to external uncontrollable factors and to poorly known parameters, whose presence tends to blur some fundamental underlying regularities. In this paper we consider that complexity might be an intrinsic property generated by the nonlinear character of the system's dynamics. Bifurcations, chaos and fractals, three important mechanisms leading to complex behaviour in nonlinear dynamical systems, are reviewed and the role of the theory of nonlinear dynamical systems as a major tool of interdisciplinary research in geosciences is stressed. The general ideas are illustrated on the dynamics of fluctuation-induced transitions between multiple climatic states with special emphasis on Quaternary glaciations.