A sandpile is a configuration of grains on the square lattice. A site with at least four grains topples, sending one grain to each of its neighbors, and adding a single grain can set off an avalanche of topplings.

Bak, Tang, and Wiesenfeld (1987) introduced this model as an example of self-organized criticality. In a finite box whose boundary absorbs grains, adding grains at random sites defines a Markov chain, and Athreya and Járai

(2004) showed that its stationary distributions converge to a stationary state on the whole lattice. They asked: if we add one grain to this state, does the avalanche stop? Járai and Redig (2008) proved that it does in dimensions three and higher, using the transience of random walk. On the other hand, in two dimensions the expected number of topplings at the origin is infinite. I will discuss a recent proof showing that sandpile avalanches in two dimensions are finite.