ABSTRACT: Mike Hill, Mike Hopkins and I have recently solved the Arf-Kervaire invariant problem. Our main theorem states that θj does not exist for j > 6. θj is a hypothetical element of order 2 in the stable homotopy groups of spheres in the (2^(j+1)-2)-stem. It was previously known to exist for j < 6. The status of θ6 (in the 126-stem) remains open. I will discuss the history of the problem and outline our methods for solving it.