The geometric, topological and analytic implications of scalar curvature constraints have been an active area of research for many years. In 1998, Thomas Schick discovered a purely homological obstruction to the existence of positive scalar curvature metrics on oriented closed smooth manifolds in terms of torality properties of their fundamental classes. We will revisit this obstruction and provide a group homological formulation. As an application we construct new examples of manifolds which do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics. Several fundamental questions remain open. The most important is whether toral manifolds of dimension at least 4 with finite fundamental groups of odd order admit positive scalar curvature metrics. This talk is based on joint work with Misha Gromov.