  We first show that existence results due to Kazdan-Warner and Cruz-Vit\'orio
can be extended to the category of manifolds with an isolated conical
singularity. More precisely, we check that, under suitable conditions on the
link manifold, any bounded and smooth function which is negative somewhere is
the scalar curvature of some conical metric (with the boundary being minimal
whenever it is non-empty). By way of comparison, we complement this analysis by
indicating how index theory, as developed by Albin-Gell-Redman, may be used to
transfer to this conical setting some of the classical obstructions to the
existence of metrics with positive scalar curvature in the spin context. In
particular, we use a version of the notion of infinite $K$-area to obstruct
such metrics.
