This project is focused on three related topics in the field of higher-dimensional complex dynamics : bifurcations, wandering domains, and parabolic dynamics. Each of these topics has gone through recent breakthroughs by members of the project. Bifurcation theory in higher dimensions has been developped only recently. We intend to address e.g. the following questions: are bifurcation loci homegeneous, or are there stronger bifurcation sub-loci ? Can we extend the existing theory to wider classes of dynamical systems ? The first examples of wandering domains for two important classes of maps have been recently constructed by the scientific coordinator and two other members of the project. We plan to better describe the associated possible dynamics, and their repartition in parameter spaces. Finally, parabolic implosion techniques have been used crucially in one construction of wandering domains. We plan to contribute to the further development of these techniques.