Background and Aims A strong correlation exists between smoking and the use of alcohol and cannabis. This paper uses polygenic risk scores to explore the possibility of overlapping genetic factors. Those scores reflect a combined effect of selected risk alleles for smoking. Methods Summary‐level P‐values were available for smoking initiation, age at onset of smoking, cigarettes per day and smoking cessation from the Tobacco and Genetics Consortium (n between 22 000 and 70 000 subjects). Using different P‐value thresholds (0.1, 0.2 and 0.5) from the meta‐analysis, sets of ‘risk alleles’ were defined and used to generate a polygenic risk score (weighted sum of the alleles) for each subject in an independent target sample from the Netherlands Twin Register (n = 1583). The association between polygenic smoking scores and alcohol/cannabis use was investigated with regression analysis. Results The polygenic scores for ‘cigarettes per day’ were associated significantly with the number of glasses alcohol per week (P = 0.005, R2 = 0.4–0.5%) and cannabis initiation (P = 0.004, R2 = 0.6–0.9%). The polygenic scores for ‘age at onset of smoking’ were associated significantly with ‘age at regular drinking’ (P = 0.001, R2 = 1.1–1.5%), while the scores for ‘smoking initiation’ and ‘smoking cessation’ did not significantly predict alcohol or cannabis use. Conclusions Smoking, alcohol and cannabis use are influenced by aggregated genetic risk factors shared between these substances. The many common genetic variants each have a very small individual effect size.