Spin${}^h$ Manifolds

The concept of a ${\mathrm{S}\mathrm{p}\mathrm{i}\mathrm{n}}^h$-manifold, which is a cousin of Spin- and ${\mathrm{S}\mathrm{p}\mathrm{i}\mathrm{n}}^c$-manifolds, has been at the center of much research in recent years. This article discusses some of the highlights of this story.