This is the second and concluding part of a survey article. Whether or not a smooth manifold admits a Riemannian metric whose scalar curvature function is strictly positive is a problem which has been extensively studied by geometers and topologists alike. More recently, attention has shifted to another intriguing problem. Given a smooth manifold which admits metrics of positive scalar curvature, what can we say about the topology of the space of such metrics? We provide a brief survey, aimed at the nonexpert, which is intended to provide a gentle introduction to some of the work done on these deep questions.