  We present a review of photonic implementations of discrete-time quantum
walks (DTQW) in the spatial and temporal domains, based on spatial- and
time-multiplexing techniques, respectively. Additionally, we propose a detailed
novel scheme for photonic DTQW, using transverse spatial modes of single
photons and programmable spatial light modulators (SLM) to manipulate them.
Unlike all previous mode-multiplexed implementations, this scheme enables
simulation of an arbitrary step of the walker, only limited, in principle, by
the SLM resolution. We discuss current applications of such photonic DTQW
architectures in quantum simulation of topological effects and the use of
non-local coin operations based on two-photon hybrid entanglement.
