In 2008 the Large Hadron Collider (LHC) and its experiments started operation at the European Centre of Nuclear Research (CERN) in Geneva with the main aim of finding or excluding the Higgs boson. Only four years later, on the 4th of July 2012, the discovery of a Higgs-like particle was proven and first published by the two main experiments ATLAS and CMS. Even though proton–proton collisions are the main operation mode of the LHC, it also acts as an heavy-ion collider. Here, the term “heavy-ion collisions” refers to the collision between fully stripped nuclei. While the major hardware system of the LHC is compatible with heavy-ion operation, the beam dynamics and performance limits of ion beams are quite different from those of protons. Because of the higher mass and charge of the ions, beam dynamic effects like intra-beam scattering and radiation damping are stronger. Also the electromagnetic cross-sections in the collisions are larger, leading to significantly faster intensity decay and thus shorter luminosity lifetimes. As the production cross-sections for various physics processes under study of the experiments are still small at energies reachable with the LHC and because the heavy-ion run time is limited to a few days per year, it is essential to obtain the highest possible collision rate, i.e. maximise the instantaneous luminosity, in order to obtain enough events and therefore low statistical errors. Within this thesis, the past performance of the LHC in lead-lead (Pb-Pb) collisions, at a centre-of-mass energy of 2.76 TeV per colliding nucleon pair, is analysed and potential luminosity limitations are identified. Tools are developed to predict future performance and techniques are presented to further increase the luminosity. Finally, a perspective on the future of high energy heavy-ion colliders is given.