Abstract Background Recent well-powered genome-wide association studies have enhanced prediction of substance use outcomes via polygenic scores (PGSs). Here, we test (1) whether these scores contribute to prediction over-and-above family history, (2) the extent to which PGS prediction reflects inherited genetic variation v. demography (population stratification and assortative mating) and indirect genetic effects of parents (genetic nurture), and (3) whether PGS prediction is mediated by behavioral disinhibition prior to substance use onset. Methods PGSs for alcohol, cannabis, and nicotine use/use disorder were calculated for Minnesota Twin Family Study participants (N = 2483, 1565 monozygotic/918 dizygotic). Twins' parents were assessed for histories of substance use disorder. Twins were assessed for behavioral disinhibition at age 11 and substance use from ages 14 to 24. PGS prediction of substance use was examined using linear mixed-effects, within-twin pair, and structural equation models. Results Nearly all PGS measures were associated with multiple types of substance use independently of family history. However, most within-pair PGS prediction estimates were substantially smaller than the corresponding between-pair estimates, suggesting that prediction is driven in part by demography and indirect genetic effects of parents. Path analyses indicated the effects of both PGSs and family history on substance use were mediated via disinhibition in preadolescence. Conclusions PGSs capturing risk of substance use and use disorder can be combined with family history measures to augment prediction of substance use outcomes. Results highlight indirect sources of genetic associations and preadolescent elevations in behavioral disinhibition as two routes through which these scores may relate to substance use.