  This work is originally a Cambridge Part III essay. Throughout the paper,
some aspects of General Relativity in higher dimensions are reviewed. The work
presented draws a path within the wide landscape of higher dimensional black
holes theory towards a specific objective: understanding how the combination of
extended black objects and ultra-spinning rotation dynamics give rise to black
hole topologies that depart from sphericity. The discussion aims to offer a
compromise between giving a reasonably wide picture of the area of higher
dimensional black holes, while at the same time going into detailed
calculations that make manifest the enhanced nature of General Relativity in
$d>4$.
