This study examines cognitive functioning in adults born across the range of prematurity with appropriate or small for gestational age (SGA) birth weight compared with full-term controls.ESTER Preterm Birth Study participants without severe disabilities, comprising 133 early preterm (<34 weeks, 17% SGA), 241 late preterm (34 + 0-36 + 6 weeks, 13% SGA), and 348 full-term subjects, performed the Cogstate® test at a mean age of 23.3 (SD = 1.2) years. Subtests measured paired associate learning, psychomotor function, executive function, spatial memory efficiency, visual memory, attention, working memory, visual learning, and emotional cognition. Data were analyzed with linear regression, full models adjusted for prenatal and postnatal factors and socioeconomic position.Early preterm, late preterm, and full-term participants showed similar abilities in almost all subtests. Early preterm participants had 0.6 fewer moves/10 s (95% CI: -1.0; -0.2, full model) and late preterm and SGA participants had 1.3 fewer moves/10 s (95% CI: -2.1; -0.4) than full-term controls in the Groton Maze Learning Test, indicating weaker spatial memory efficiency.Adults born across the range of prematurity on average lack major defects in cognitive abilities. Cognitive problems may persist to adulthood only among those born the smallest: very preterm or preterm and SGA.Although preterm birth is a risk for the developing brain, adults born preterm as a group showed similar cognitive performance to their full-term peers.Children born preterm across gestational ages show defects in cognitive domains. With a supportive environment, many of them have the potential to catch up with those born at term.The unfavorable effect of late preterm birth on cognitive functions in childhood may not persist to adulthood; in this study, adults born late preterm showed similar cognitive functioning to adults born full-term.The deficits in cognitive function in adults born preterm detected by earlier studies mainly concern those born the smallest, i.e., very preterm or preterm and small for gestational age.