Substance use disorders (SUDs) are conditions in which the use of legal or illegal substances, such as nicotine, alcohol or opioids, results in clinical and functional impairment. SUDs and, more generally, substance use are genetically complex traits that are enormously costly on an individual and societal basis. The past few years have seen remarkable progress in our understanding of the genetics, and therefore the biology, of substance use and abuse. Various studies - including of well-defined phenotypes in deeply phenotyped samples, as well as broadly defined phenotypes in meta-analysis and biobank samples - have revealed multiple risk loci for these common traits. A key emerging insight from this work establishes a biological and genetic distinction between quantity and/or frequency measures of substance use (which may involve low levels of use without dependence), versus symptoms related to physical dependence. In this Review, Gelernter and Polimanti discuss how recent large-scale studies have provided insights into the genetics and biology of substance use and abuse. By considering a range of addictive substances (both legal and illegal), they describe the genetic commonalities and distinctions among use and dependency phenotypes for these substances.