In 1982, Feynman, considered the possibility of using cellular automata (CAs) both as models of quantum systems and as quantum computer architecture, driven by the fact that CAs are a model for universal computation. Yet, their quantum counterpart, quantum cellular automata (QCAs), are limited by the no-coning theorem and the no-go lemma and thus, except for the trivial case, do not constitute a universal computational model. To overcome this obstacle, we consider discrete-time quantum walks which reproduce unitary evolution in space and have been proven to be a universal quantum computation model. By combining them with quantum cellular automata, which reproduce unitary evolution in time, a new model of quantum computation is possible. In this chapter, we formulate discrete-time quantum walks on QCAs and present various applications that are different in nature, to emphasize the universality of the model.