In the Large Hadron Collider (LHC), particle physics events are created by colliding high energy proton beams at a number of interaction points around the ring. One of the main performance indicating parameters of the LHC is the luminosity. The luminosity is limited by, amongst other things, the strength of the beam-beam interaction. In this thesis, the effect of the beam-beam interaction on the luminosity performance of the LHC and the proposed High Luminosity Large Hadron Collider (HL-LHC) is investigated. Results from a number of dedicated, long-range beam-beam machine studies are presented and analysed. In these studies, the minimum beam-beam separation for two different beta starÂ optics are identified. This separation defines the minimum operational crossing angle in the LHC. The data from these studies are then compared to simulation of the dynamic aperture and the results are discussed. In addition to studies of the LHC, an analytical approach is derived in order to describe the hourglass effect, which may become a contributing factor in limiting the luminosity performance of the HL-LHC.