Abstract: In this talk, I will describe two distinct strategies for trapping Majorana zero modes (MZMs) with superconducting vortices. There exists a common belief that for s-wave superconductors, the existence of normal-state band topology, such as the topological Dirac surface state, is crucial for inducing vortex MZMs. We recently uncovered a striking example where nontrivial vortex Majorana physics arises in a trivial s-wave superconductor with a trivial normal state. This further leads to a prediction of highly unusual vortex topological behaviors in superconducting HgTe-class materials. For the second part, I will discuss new possibilities of vortex MZMs in topological superconductors (TSCs). Despite the well-known Read-Green paradigm of chiral TSCs, there have been surprisingly few research efforts to explore vortex response in non-chiral TSC systems. We recently found that 2D class-D Cn-protected higher-order TSCs will universally trap a pair of vortex MZMs as a topological response. The two MZMs living inside the same vortex carry distinct angular momentum and are hence protected by Cn. This new paradigm will shed new light on the experimental detection of crystalline topological physics in superconductors.