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A large body of scientific evidence gathered in the last few decades shows the relevance of dynamical and stochastic phenomena in nonlinear systems. In some areas, such as biophysics, most of this evidence has been theoretical, and only recently experimental techniques have become available that will provide the data needed to test the theoretical predictions made. In other areas, such as materials science and photonics, experimental techniques are better established, but challenging open questions remain. Our goal is to address some of these questions in a coordinated way, using our expertise in statistical and nonlinear physics, and closely in connection with experimental work done either within the group or with external collaborators.