Peg solitaire on graphs - A survey

One decade ago, Beeler and Hoilman introduced the game of peg solitaire to arbitrary graphs. Since then, some progress has been made characterizing solvable graphs. Furthermore, several variants of the original game have been considered. The main goal of this paper is to give a proper overview of the results that have been obtained so far (until December 2021) as well as to show which methods are used to prove these. We also present important open questions and research directions, including some new results. The content should be helpful to mathematicians already interested in this topic, but, on the other hand, will provide a perfect starting point for (also early career) researchers looking for a fruitful topic in combinatorial game theory.