This PhD thesis is entirely focused on classical and thermodynamical aspects of black hole physics. Black holes are present in a wide variety of fields and their study is of importance not only to astrophysics but also to theoretical physics. In this thesis we have developed four different projects, each one of them focused in a specific kind of black hole. * Higher dimensional black branes and their dynamic and thermodynamic instabilities. Using the blackfold effective theory for black branes we have refined the relation between the dynamic and thermodynamic instabilities present in black branes. * Stationary black hole horizons with a temperature gradient along them that remains constant in time. Inspired by black funnel solutions present in the context of AdS/CFT, we have constructed analytically the event horizon of a flowing solution whose horizon resembles a thin black funnel. * New families of six dimensional rotating black holes: bumpy black holes. We have expanded the understanding of the space of stationary solutions in six dimensions by constructing numerically six families of solutions and analysing their properties. * Exact event horizon of a black hole merger. Black hole mergers have traditionally been part of the field of numerical General Relativity. We have been able to construct analytically the event horizon of a black hole merger in which one of the black holes is much bigger than the other. With the event horizon some critical behaviours that may be universal in black hole mergers have been described.