In this thesis we have made progress on the study of higher dimensional gravity by focusing on the properties of black holes and branes and their dynamics. We will present two main projects. First we provide several maps between different spacetimes. In particular, we will show a mathematical correspondence, called AdS/dS map, which relates spacetimes with negative and positive cosmological constant, including scalar matter, based on a generalized dimensional reduction. This correspondence may possibly give hints to improve our understanding of holography in dS space. We will moreover present a new Kerr/AdS solution with hyperbolic horizon obtained from a known Kerr/dS one through the map. In the second part, we will study the hydrodynamics properties of different charged black branes, solutions of Einstein-Maxwell-dilaton theory. We focus on Kaluza Klein black branes, fundamentally charged (dilatonic) black branes and branes with Maxwell charge smeared over their worldvolume. We will show the transport coefficients extracted from the effective stress energy tensor of the fluid associated to those branes determining, hence, their dissipative behaviour. For the latter two classes of charged black branes we will also present the dynamical stability analysis obtained studying the response to small long-wavelength perturbations.