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A brief history of planar aperiodic tile sets is presented, starting from theDomino Problem proposed by Hao Wang in 1961. We provide highlights that led tothe discovery of the Taylor--Socolar aperiodic monotile in 2010 and the Hat andSpectre aperiodic monotiles in 2023. The Spectre tile is an amazingly simplemonotile; a single tile whose translated and rotated copies tile the plane butonly in a way that lacks any translational periodicity. We showcase thisbreakthrough discovery through the 60$+$ years that aperiodic tile sets havebeen considered.

Planar aperiodic tile sets: from Wang tiles to the Hat and Spectre monotiles