Primates are bred in captivity for a number of purposes, from zoo-based captive breeding programmes for conservation to breeding for biomedical research. In each case, breeding animals that are fit for purpose, either as viable candidates for reintroduction or as valid research models, has presented challenges and resulted in steep learning curves. The breeding of animals for biomedical research has become increasingly focused on the production of animals that are less stressed by captive (specifically laboratory) environments. This is because elevated, particularly chronic, stress responses can result in altered physiological, neurological and behavioural states that have the potential to compromise the validity of scientific results. Selective breeding in captivity to, for example, maximise production, select for docile temperament or specific genotypes for biomedical research, is likely to be counter to natural selective pressures for evolutionary fitness. Given that many natural selective pressures active in the wild are absent in captivity, this paper reviews the selective breeding of primates (especially Old World monkeys) in captivity, its potential negative effects, and options that exist for ameliorating these negative effects.