Aperiodic tilings of a plane

Back in the beginning of 1960, Hao Wan posed the following question: given a collection of square tiles with colored edges, fill a plane with their shifted copies so that every edge common to two tiles also has a common color. This is sometimes possible and sometimes not. If such a tiling exists, does there also exist a periodic tiling (here periodicity is defined by requiring that a tiling maps to itself when shifted by a certain vector)? A negative answer to that question was given by Berger in 1966, and many other aperiodic tilings have been constructed since then. The talk will include the history of this problem and present constructions of certain aperiodic tilings.