A brief history of planar aperiodic tile sets is presented, starting from the
Domino Problem proposed by Hao Wang in 1961. We provide highlights that led to
the discovery of the Taylor--Socolar aperiodic monotile in 2010 and the Hat and
Spectre aperiodic monotiles in 2023. The Spectre tile is an amazingly simple
monotile; a single tile whose translated and rotated copies tile the plane but
only in a way that lacks any translational periodicity. We showcase this
breakthrough discovery through the 60+ years that aperiodic tile sets have
been considered.Comment: Expositor