Photons can be characterized by multiple physical properties (such as frequency, linear momentum, polarization, etc.) which can all be exploited to encode quantum information or to define quantum variables. Among them, we focus our attention on transverse spatial modes of light, that are paraxial optical fields showing specific amplitude and phase profiles in the plane perpendicular to the main propagation direction. A remarkable example is provided by helical modes, carrying a definite amount of orbital angular momentum. In our group we engineer photonic platforms where we dynamically manipulate spatial and polarization properties of these optical modes, so as to tailor photonic evolutions that mimic quantum models of interest. Our simulators can be shaped to implement quantum dynamics such as quantum walks, in one and two spatial dimensions. Our systems are carefully designed to manifest photonic topological phases, offering an ideal context where related phenomena can be discovered and deeply investigated. We are also interested in the simulation of these processes in a genuinely quantum regime, obtained when considering the evolution of multiple correlated photons.