Moiré patterns are commonly observed in layered systems of 2D materials such as graphene, h-BN, MoS2, etc, or when 2D materials are grown on crystalline metal substrates. To understand moiré patterns, we introduce the concept of interlayer or van der Waals (vdW) dislocations, and show that arrays of these defects constitute the moiré patterns associated with regions of commensurability and incommensurability between the layers. We note that moiré patterns and the defects appearing therein are electronic structure objects formed by weak interactions between the layers, locked into place by strong in-plane interactions in the constituent layers. We explain the variety of experimentally observed moiré phenomena, including the distinct moiré patterns formed by various combinations of 2D materials on the same metal support layers, as well as point and line defects in moiré patterns. We then discuss the connection between vdW dislocations and several microstructural observations in 2D materials synthesis, including the distribution of angles and the formation of grain boundaries in polycrystalline 2D material layers.