Persistent homology is a tool for studying robustness of topological features in topological spaces. It is defined as a graded module on a polynomial ring k[x] with one variable, where k is a field. From the structure theorem of modules on k[x], the persistnet homology has a unique decomposition into indecomposables, and this decomposition encodes information of robustness of topological features as persistent diagrams. The persistent homology can be also treated as a represetation on the An-quiver. In this talk, we briefly review the theory and computations of persistent homology, and then generalize them to certain types of quivers. Moreover, several applications on protein structural analysis are also discussed.