AbstractStudents’ socioeconomic status (SES) is central to much research and policy deliberation on educational inequalities. However, the SES model is under severe stress for several reasons. SES is an ill‐defined concept, unlike parental education or family income. SES measures are frequently based on proxy reports from students; these are generally unreliable, sometimes endogenous to student achievement, only low to moderately intercorrelated, and exhibit low comparability across countries and over time. There are many explanations for SES inequalities in education, none of which achieves consensus among research and policy communities. SES has only moderate effects on student achievement, and its effects are especially weak when considering prior achievement, an important and relevant predictor. SES effects are substantially reduced when considering parent ability, which is causally prior to family SES. The alternative cognitive ability/genetic transmission model has far greater explanatory power; it provides logical and compelling explanations for a wide range of empirical findings from student achievement studies. The inadequacies of the SES model are hindering knowledge accumulation about student performance and the development of successful policies.Context and implicationsRationale for this studyThis review was written in response to the disconnect between the literature surrounding student achievement studies, and the cognitive psychology and behavioural genetic academic literatures. It is well‐established that student achievement is closely related to cognitive ability and both have sizable genetic components, findings largely ignored in achievement studies. This review’s aim is for more considered responses to socioeconomic inequalities in student achievement by both researchers and policymakers.Why the new findings matterThe review provides overwhelming evidence that much of the current thinking about SES and student achievement is mistaken.Implications for researchers and policymakersThe current emphasis on SES is misleading and wastes considerable human and financial resources that could much better be utilized. The focus should be on student performance ensuring that low achievers have rewarding educational and occupational careers, and raising the overall skill levels of students, not on the nebulous, difficult to measure, concept of SES, which is only moderately associated with achievement.