We will introduce the Stolz sequence and explain how it plays a role in the study of metrics with positive scalar curvature. We shall then extend it to two different contexts: that of (G, F)-spaces, i.e., proper G-spaces with isotropy groups belonging to a family F of subgroups of G, and that of manifolds with non-isolated singularities. In both cases, the sequence is studied for appropriate classes of metrics with positive scalar curvature, and it is shown, in particular, how the Stolz R-groups have a strict dependence on the 2-skeleton. Subsequently, the mapping of the Stolz sequence to the Higson-Roe analytic surgery sequence in the singular setting with (L,G)-singularities will be explained. This will then be used in order to provide a lower bound on the rank of the bordism group of these psc metrics.