Graph pebbling is a game played on a graph with any number of pebbles on each vertex. A pebbling move consists of choosing a vertex \(v\) that has at least two pebbles, removing two pebbles from \(v\), and placing one pebble on one of \(v\)'s neighbors (the other pebble is discarded). Before play begins, a target vertex is chosen. The object of the game is to move one pebble onto the target vertex through a sequence of pebbling moves. This talk will focus on a variation in which graph pebbling is viewed as a two-player, impartial combinatorial game. Instead of moving to a target vertex, the objective is to be the last player to make a valid move. We will consider the game played on various classes of graphs, including cycles and complete graphs. We will also consider variations of the pebbling move. In each case, we are interested in which positions are winning positions in optimal play.