The thesis will describe the state of the art in calculations, simulations and measurement of wakefields in collimators. I will present a wide ranging summary of work completed over t he last five years. I will introduce improved methods for the analytical calculation of wakefields and I will apply these to calculate higher order corrections to taper profiles in the inductive regime. I will outline a prescription for calculating wakefield kick factors, including estimates of errors normally unavailable with the FDTD method, and will demonstrate this using the GdfidL software. I will perform an optimisation of the electromagnetic properties of a complete collimator and its structure. I will compare these calculations with experimental data taken at End Station A at SLAC, and discuss the limitations of these and non beam-based experimental measurements