Large impact craters collapse to form complex structures, with zones of structural uplift that can be expressed topographically as central peaks and/or peak-rings internal to the crater rim. The formation of these structures requires transient strength reduction in the target material, but the process that facilitates this strength reduction is unknown. More fundamentally, descriptions of how structural uplifts, particularly peak-rings, are emplaced lack the quantitative details needed to constrain models of large impact crater formation. This thesis describes aspects of the formation of complex impact structures in an attempt to constrain the mechanism that facilitates crater collapse. The approach adopted in this research was to combine geological observations of large impact structures; field geology, core logging, petrography, and petrophysics, with the results of numerical impact simulations. More specifically, this thesis focusses upon the Clearwater Lake impact structures and the Chicxulub impact structure as case studies to understand complex crater collapse. The results presented demonstrate that the block model of acoustic fluidisation provides a realistic description of the rheology of rocks during crater collapse. Nonetheless, observational support for the block model of acoustic fluidisation, or indeed, any single currently proposed transient weakening mechanism, is lacking. Deformation during crater collapse is dominated by cataclasites which occur on a variety of scales, while the lubrication of faults by frictional melts and/or intrusions of impact melt and breccia may only have a significant effect during the late-stages of crater modification. The research carried out in this thesis demonstrates numerous ways in which geological and geophysical observations can be combined with numerical impact simulations to understand cratering and constrain the process of crater collapse. The methods include using observationally constrained shock pressures, geophysical data, and most significantly, the structural history of rocks in impact craters.