We use PIAAC data to study the relationship between parental education and educational success among adults from 23 advanced economies. We consider educational success in terms of both educational "attainment" (formal qualifications) and educational "achievement" (competencies) and in both "absolute" and "relative" terms (i.e. as the individual's rank in the distribution of educational success). Parental education effects are stronger for educational attainment than for achievement in all countries. Cross-national variation in the strength of social background effects follows broadly similar patterns for the different ways of measuring success, but a few countries combine relatively strong achievement with relatively weak attainment effects and "vice versa." Tracking in secondary education is associated with stronger background effects for educational attainment but not for achievement. Greater prevalence of formal (non-formal) AET is associated with stronger (weaker) background effects for both attainment and achievement, while vocational orientation of upper secondary education does not matter much.