Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more naturally to some physical implementations, such as linear optics. Numerous authors have considered walks with one or two walkers, on one-dimensional graphs, and several experimental demonstrations have been performed. In this paper, we discuss generalizing the model of discrete time quantum walks to the case of an arbitrary number of walkers acting on arbitrary graph structures. We present a formalism that allows for the analysis of such situations, and several example scenarios for how our techniques can be applied. We consider the most important features of quantum walks-measurement, distinguishability, characterization and the distinction between classical and quantum interference. We also discuss the potential for physical implementation in the context of linear optics, which is of relevance to present-day experiments.