**7. Conclusions**

In this Book Chapter, we reported a review of novel approaches to photonic discrete-time quantum walk (DTQW) platforms. Namely, we discussed implementations via spatial-multiplexing or temporal-multiplexing schemes, and we introduced a novel scheme for implementations based on transverse spatial modes of photons, which are in turn controlled by spatial light modulators (SLMs). While the number of discrete time-steps (*n*) that can be experimentally implemented via mode multiplexed approaches is typically limited by the mode scaling of the multiplexed technique itself, i.e., 2*n* þ 1 for spatial mode multiplexing and 2*<sup>n</sup>* for temporal-mode multiplexing, realizations using transverse modes can in principle enable experimental simulation of an arbitrary temporal step *n*, only limited by the resolution of the SLM itself. We present several relevant applications of DTQWs in quantum simulation. Namely, for the simulation of topological effects, ascribed to each DTQW platform. Specifically, in the context of modemultiplexed DTQWs, we presented in detail the calculation of the Zak Phase, corresponding to the Berry phase across the Brillouin zone, for the case of the *split-step* DTQW and for the case of DTQW with non-commuting rotations, which are implemented via spatial and temporal mode-multiplexing, respectively.
