The generation of high-energy-density plasmas by the electromagnetic implosion of cylindrical foils (i.e., imploding plasma shells or hollow z-pinches) has been explored analytically and through numerical simulation. These theoretical investigations have been performed for a variety of foil initial conditions (radius, height, and foil mass) for both capacitive and inductive pulsed power systems. The development of the theoretical modeling techniques is presented, covering both circuit models and plasma load models. The circuit models include simple single loop capacitive and multiple loop inductive systems. These circuits are coupled to the imploding plasma loads whose response has been studied by models ranging from simple time varying inductances to complex two-dimensional magnetohydrodynamic numerical simulations. Results from a series of configurations are given, showing the development of modelling techniques used to study the dynamics of the plasma implosion process and the role of instabilities. Interaction between analytic techniques and detailed numerical simulation has led to improvement in all theoretical modeling techniques presently used to study the implosion process. Comparisons of implosion times, shell structure, instability growth rates, and thermalization times have shown good agreement between analytic/heuristic techniques and more detailed two dimensional magnetohydrodynamic simulations. These in turn have provided excellent agreement with experimental results for both capacitor and inductor pulse power systems.