Let $\Gamma_1$, $\Gamma_2$ be two graphs with $n$ vertices. Is there a bijection from the set of vertices of $\Gamma_1$ to that of $\Gamma_2$ sending $\Gamma_1$ to $\Gamma_2$? If such bijections exist, they form a coset $H\cdot \pi$ in the symmetric group on $n$ elements. How can one find a representative $\pi$ and a set of generators for $H$?. Finding an algorithm that answers such questions efficiently (in all cases) is a challenge that has long remained open. Babai has recently shown how to solve these problems and related ones in quasipolynomial time, i.e., time $O\left(\exp\left((\log n)^C\right)\right)$, where $C$ is a constant. His strategy is based in part on an algorithm due to Luks (1980/82), who solved the case of graphs of bounded degree.