Moire lattices consist of two superimposed identical periodic structures with a relative rotation angle. Moire lattices have several applications in everyday life, including artistic design, the textile industry, architecture, image processing, metrology and interferometry. For scientific studies, they have been produced using coupled graphene-hexagonal boron nitride monolayers(1,2), graphene-graphene layers(3,4) and graphene quasicrystals on a silicon carbide surface(5). The recent surge of interest in moire lattices arises from the possibility of exploring many salient physical phenomena in such systems; examples include commensurable-incommensurable transitions and topological defects(2), the emergence of insulating states owing to band flattening(3,6), unconventional superconductivity(4) controlled by the rotation angle(7,8), the quantum Hall effect(9), the realization of non-Abelian gauge potentials(10) and the appearance of quasicrystals at special rotation angles(11). A fundamental question that remains unexplored concerns the evolution of waves in the potentials defined by moire lattices. Here we experimentally create two-dimensional photonic moire lattices, which-unlike their material counterparts-have readily controllable parameters and symmetry, allowing us to explore transitions between structures with fundamentally different geometries (periodic, general aperiodic and quasicrystal). We observe localization of light in deterministic linear lattices that is based on flatband physics(6), in contrast to previous schemes based on light diffusion in optical quasicrystals(12), where disorder is required(13) for the onset of Anderson localization(14) (that is, wave localization in random media). Using commensurable and incommensurable moire patterns, we experimentally demonstrate the twodimensional localization-delocalization transition of light. Moire lattices may feature an almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool for controlling the properties of light patterns and exploring the physics of periodic-aperiodic phase transitions and two-dimensional wavepacket phenomena relevant to several areas of science, including optics, acoustics, condensed matter and atomic physics.