Binary black hole solutions of General Relativity can be generated through the application of known generating techniques, as long as the solutions are stationary and axisymmetric, either in four and five-dimensions. After reviewing the construction of the double Kerr solution and of the black Saturn system, I will summarize the properties of each black hole/ring in binary systems and discuss their physical interpretation. In particular, it is possible to observe that the angular velocity of a black hole or a fat black ring, with intrinsic angular momentum, always decreases in the presence of a neighbour black hole. Curiously, this slow down allows black holes and fat black rings to carry more angular momentum than an isolated one with the same mass, without reaching the extremal limit.