Event reconstruction in particle detectors transforms detector signals into physics objects and, in large particle detectors, generally involves track reconstruction, vertex reconstruction, object reconstruction, and object identification. Vertex reconstruction typically involves two steps: clustering reconstructed tracks into vertex candidates, or seeds, and fitting the vertex candidates to obtain vertex parameters. Secondary vertices are used in the identification, or tagging, of displaced jets originating from b and c quark hadronization, and in the tagging of soft jets with low transverse momenta. Displaced vertices are used in the reconstruction of long-lived particles. These proceedings present an overview of methods used by the CMS experiment for offline secondary and displaced vertex reconstruction during Runs 1 to 3 of the LHC. In the Phase 2 upgrade of the CMS detector for the High-Luminosity LHC operation, changes to the triggering system and track reconstruction will affect the performance of secondary vertex reconstruction, which has not undergone major revision since Run 2. Potential methods aimed at improving the baseline performance in Run 3 and Phase 2 are discussed.