Background: Cognitive training helps to promote healthy aging and ease activities of daily living for older adults. Recently, experiments have been conducted using robots to perform this cognitive training. Methods: A review was conducted to examine the effects of computer-based cognitive interventions for older adults who were either healthy or experiencing mild cognitive impairment (MCI). A second study also examined the evolution of socially assistive robots (SAR) and their effectiveness at administering cognitive training for older adults. Results: Eighty-one studies published between 2009 and 2019 were identified for review, 56 of which focused on computerized cognitive training (CCT) while 25 examined the use of robotics. Twenty-four of the 56 CCT studies met the inclusion criteria. These were further classified into two groups: studies which used self-designed programs, and studies using commercially available ones. Of the 25 studies examining the use of robotics in cognitive intervention 7 met the inclusion criteria. Review shows that CCT improves cognitive function but that robots are more effective tools for improving cognition. Conclusion: It can be concluded that CCT is beneficial for older adults and though there are drawbacks to this approach they are overcome by the introduction of robots into the training process. Culture, language, and socio-economic considerations vis-a-vis robot design and training methodology should be included in future research.