Abstract: A graph is a collection of nodes connected by edges. In this talk I’ll present a family of chip-firing games, which start with a placement of chips on the nodes of a graph. After placing the chips, we move them around by “firing” a node, meaning it donates a chip to each of its neighbors. This leads to many mathematical questions: Given two placements of chips, can we move between them using a sequence of chip-firing moves? If so, what’s the fastest way? It not, how can we prove it’s impossible? And if some of the nodes start with a negative number of chips, can we perform chip-firing moves to get those nodes out of debt? This talk will showcase many results and open questions about these chip-firing games, including new theorems proved by undergraduates in Summer 2018.