We rely on observations of occurrences of fossils to infer the rates and timings of origination and extinction of taxa. These estimates can then be used to shed light on questions such as whether extinction and origination rates have been higher or lower at different times in earth history or in different geographical regions, etc. and to investigate the possible underlying causes of varying rates. An inherent problem in inference using occurrence data is one of incompleteness of sampling. Even if a taxon is present at a given time and place, we are guaranteed to detect or sample it less than 100% of the time we search in a random outcrop or sediment sample that should contain it, either because it was not preserved, it was preserved but then eroded, or because we simply did not find it. Capture-mark-recapture (CMR) methods rely on replicate sampling to allow for the simultaneous estimation of sampling probability and the parameters of interest (e.g. extinction, origination, occupancy, diversity). Here, we introduce the philosophy of CMR approaches especially as applicable to paleontological data and questions. The use of CMR is in its infancy in paleobiological applications, but the handful of studies that have used it demonstrate its utility and generality. We discuss why the use of CMR has not matched its development in other fields, such as in population ecology, as well as the importance of modelling the sampling process and estimating sampling probabilities. In addition, we suggest some potential avenues for the development of CMR applications in paleobiology.