We will discuss various situations where a certain perturbation of the Dirac operator on spin manifolds can be used to obtain distance estimates from lower scalar curvature bounds. A first situation consists in an area non-decreasing map $f$ from a Riemannian spin manifold with boundary $X$ into the round sphere under the condition that the map is locally constant near the boundary and has nonzero degree. Here a positive lower bound of the scalar curvature is quantitatively related to the distance between the support of the differential of $f$ and the boundary of $X$. A second situation consists in estimating the distance between the boundary components of Riemannian “bands” $M×[−1,1]$ where $M$ is a closed manifold that does not carry positive scalar curvature. Both situations originated from questions asked by Gromov. In the final part, I will compare the Dirac method with the minimal hypersurface method and show that if $N$ is a closed manifold such that the cylinder $N\times\mathbb{R}$ carries a complete metric of positive scalar curvature, then $N$ also carries a metric of positive scalar curvature. This answers a question asked by Rosenberg and Stolz. Based on joint work with Daniel Raede and Rudolf Zeidler.