Using the simplest form of an abundance estimator using tag-recapture data, the Lincoln-Petersen equation, we summarise the processes that may occur during a tagging program that lead to difficulty in accurately estimating key parameters, and consequently introduce bias into an abundance estimate. We also review the methods that have been used in CCAMLR tag recapture to program to mitigate against this bias, or to account for their effects in assessment models. In nearly all cases, examples of at sea or model-based approaches are available from established toothfish tagging programs to reduce these biases. Estimates of post-capture mortality, tag detection rates and where it occurs, post-release depredation rates are a priority for new tagging programs and tag-based assessments. Due to the complexity of toothfish movements throughout their life cycle, as well as the spatial structure of release and recapture efforts by fishing and research vessels, development of spatially explicit modelling approaches is an important next step for toothfish assessments.