As introduction to the quantum measurement problem, the debate about quantum reality is examined: Is there some objectively real world evolving deterministically, or does the success of the quantum theory preclude that notion? Since the 1920's, Einstein, Bohr, and others have struggled to reconcile their pre-conceived notions of reality with both the mathematical formalism of the theory and the counter-intuitive experimental results. Although much work has been done, no convincing arguments, or decisive experiments vindicating either point of view have been presented to date. A phenomenological model is then described, based on a random walk in probability space, which will serve as a skeleton upon which to build a more detailed model. A concrete model of quantum measurements is presented. It is based on the concept of multiple observer/participators, corresponding to special degrees of freedom, and is realized using deterministic laws for the detailed evolution of the state vectors, including chaotic dynamical maps. The consequences of the model for standard measurements are investigated, some more speculative situations are considered, and some numerical calculations are presented. Finally, the relation of the model to general physical principles and other work in the field is discussed, and a general classification for quantum measurement schemes is presented, which suggests that this model is closer in spirit and substance to the orthodox `Copenhagen' interpretation than some others are.