Quantum walks describe the evolution of quantum particles on a graph. Due to their rich dynamics, they can emulate a wide range of phenomena in real-world systems. In the first part of my talk, I will present a stable and reasonably scalable optical implementation of a discrete-time quantum walk on a line. Single photons, encoded in polarisation, walk through an interferometric network based on calcite beam displacers and half-wave plates. We demonstrate full control of the decoherence in the system and have access to all lattice sites at any given time step. This allows us to investigate a host of scenarios, such as the observation of signatures of topological phases in artificial 1D systems. We implemented phase transitions for topological phases of a certain symmetry class, distinguished by their winding number. For transitions in phase space with different topological invariants, we observe distinct bound states which are not present otherwise. In the second part of my talk, I present results on continuous-time quantum walks with periodic boundary conditions in direct-write waveguides with single photons and two-photon states.