Informally, a tiling is a covering of the plane with tiles of various shapes, arranged to avoid any overlapping. Usually, these tiles have simple shapes (e.g. polygons), and one only allows a small number of different shapes to be used for a tiling. One particularly interesting class of tiles are the so-called Wang tiles which can alternatively be represented via finite colorings of \Z^d. Given a set of such tiles, one might ask whether one can actually use them to cover the plane and whether that is possible without ever repeating oneself, i.e., without becoming periodic. The goal of this talk is to introduce (finite) colorings of Z^d, discuss their relation to Wang tiles and the domino problem, and then speak about low complexity colorings and Nivat’s conjecture.