We survey the century of work on Dehn's Group Isomorphism Problem. We begin with Adian-Rabin's proof of undecidability, see connections to graph isomorphism, and cite recent progress.

Next we focus on tools to spot patterns in groups where isomorphism is generally regarded as intractable. Using nonassociative rings we show how the problem is reduced to the study of nonsingular products. This links to questions of projective planes and higher homotopy groups of spheres.