In this thesis, we study in a model independent way models of new Physics featuring extra quarks (XQs). These quarks are predicted by several extensions of the Standard Model (SM) but have never been observed yet even though many searches have been designed to find them at the Large Hadron Collider (LHC). After an introduction about the SM and the LHC, we present the main properties of these XQs and a model independent parametrisation that can be used to describe their phenomenology with generic hypotheses about their mixing with SM quarks, both in the case of XQ coupling with SM bosons and with Dark Matter (DM) candidates. In these two cases we study the offshellness effects in pair-production and decay and show that if the Narrow-Width Approximation (NWA), that we describe in detail, is a good approximation of the full result in the small width over mass ratio limit, sizeable differences occur when the XQ width becomes larger. The conclusion of our analysis is that even though the small width assumption is always conservative it is not possible to trivially rescale the mass bounds obtained considering processes of pair production and decay in the NWA to determine constraints for XQs with large widths. We also study the role of interference in the process of pair production of new heavy XQs decaying to SM particles and show that in the NWA the interference contribution can be described by considering a parameter which contains only the relevant couplings and the scalar part of the propagators of the new quarks, both at the cross section level and at the distribution level. Finally, we study how various Supersymmetry (SUSY) searches perform for our simplified model with XQs decaying to DM. We show that cross section upper limit maps and efficiency maps obtained for stop simplified models in stop searches can also be applied to analogous XQ models, provided the NWA applies: the bound for XQs can therefore be obtained from the SUSY ones just by rescaling the exclusion with the XQ cross section.