Quantum walks describe the random walk behavior of quantum particles. When a single photon propagates in an array of coupled optical waveguides, it actually performs a quantum random walk. Photons propagating in such systems evolve in close analogy with electron transport in crystals: Both are modeled by the same tight-binding equation. This enabled in recent years the direct observations and detailed study of basic phenomena in condense matter, from Bloch Oscillations to Anderson Localization. Moreover, it led to the prediction of new phenomena resulting from the co-propagation of several quantum walkers. In this talk I shall review some of the highlights of this field, I will discuss the evolving correlations in periodic and disordered lattices, as well as recent results related to the observation of topological states in photonic quasicrystals