  Topological data analysis refers to approaches for systematically and
reliably computing abstract ``shapes'' of complex data sets. There are various
applications of topological data analysis in life and data sciences, with
growing interest among physicists. We present a concise yet (we hope)
comprehensive review of applications of topological data analysis to physics
and machine learning problems in physics including the detection of phase
transitions. We finish with a preview of anticipated directions for future
research.
