Strongly disordered quantum many-body systems can exhibit a property known as "many-body localization (MBL)" in which thermalization is inhibited. MBL systems can also exhibit topological phases, which are distinct phases of matter of MBL systems that cannot be continuously connected by varying parameters without going through a delocalization transition. MBL topological phases have previously been studied by direct correspondence with zero-temperature topological phases of non-MBL systems. However, this approach cannot fully characterize MBL topological phases. In this talk, I will argue that the right way to understand MBL topological phases is via a connection with locality preserving unitaries acting on quantum many-body systems, also known as quantum cellular automata (QCA). Moreover, I will develop the theory of the space of QCAs, putting forward a conjecture that the space of QCAs in different dimensions are related by an "Omega-spectrum" condition. This allows for topological phases of MBL systems to be classified in considerable generality. The framework can also be extended to study symmetry-protected MBL phases.