This thesis investigates the physics of various polymeric systems via the tool of computer simulation. The problems addressed include the tunable conformations of dendritic polyelectrolytes, the complexation of oppositely charged linear polyelectrolytes to charged dendrimers, the molecular mechanisms of polymer crystallization, and the retractive response of polymers perturbed from their equilibrium conformations. The algorithms employed include both equilibrium Metropolis Monte Carlo and Brownian dynamics methods. The computational investigations are augmented by scaling and variational theory treatments. The results of these studies complement experimental ventures in the respective fields and provide new insight into the limitations of existing theoretical descriptions.* *This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation).