The goals of the review are threefold: (a) to highlight the educational and employment consequences of poorly developed mathematical competencies; (b) overview the characteristics of children with mathematical learning disability (MLD) and with persistently low achievement (LA) in mathematics; and (c) provide a primer on cognitive science research that is aimed at identifying the cognitive mechanisms underlying these learning disabilities and associated cognitive interventions. Literatures on the educational and economic consequences of poor mathematics achievement were reviewed and integrated with reviews of epidemiological, behavioral genetic, and cognitive science studies of poor mathematics achievement. Poor mathematical competencies are common among adults and result in employment difficulties and difficulties in many common day-to-day activities. Among students, ∼ 7% of children and adolescents have MLD and another 10% show persistent LA in mathematics, despite average abilities in most other areas. Children with MLD and their LA peers have deficits in understanding and representing numerical magnitude, difficulties retrieving basic arithmetic facts from long-term memory, and delays in learning mathematical procedures. These deficits and delays cannot be attributed to intelligence but are related to working memory deficits for children with MLD, but not LA children. These individuals have identifiable number and memory delays and deficits that seem to be specific to mathematics learning. Interventions that target these cognitive deficits are in development and preliminary results are promising.