Even healthy older people undergo some cognitive decline with real-world consequences, although the neural plasticity persisting in older brains indicates substrates for interventions. Yet there is no consensus on cognitive interventions. The literature on cognitive training is equivocal regarding the factors important in far transfer of training to untrained abilities. That there have been few hypotheses on mechanisms underlying far transfer of training is an obstacle to the design of cognitive interventions. We evaluate two hypotheses: (1) updating and (2) distraction suppression. (1) The updating hypothesis argues that updating and monitoring of working memory representations is an important mechanism of far transfer of training. Two meta-analyses of n-back training tasks found small, but significant, effect sizes in favor of transfer to fluid intelligence (Gf) in young and older people. However, direct tests of the updating hypothesis supported only narrow transfer effects. (2) The distraction suppression hypothesis argues that suppression of irrelevant events has a central role in cognitive processing. Perceptual discrimination training improved distraction suppression, enhanced neural activity associated with task-relevant targets, suppressed neural activity associated with task-irrelevant distractions, improved brain-stem evoked potential firing patterns and “speech-in-noise” perception, transferred to working memory, and reduced risk of dementia in a large-scale study. The evidence supports the conclusion that the strongest far transfer of cognitive training would be achieved by combined updating and distraction suppression training. Even small effect sizes of transfer to Gf can be beneficial to older people, consistent with the growing evidence for the role of lifestyle factors, including educational attainment, in risk of Alzheimer’s disease.