Cardiotoxicity is a severe side effect of drugs that induce structural or electrophysiological changes in heart muscle cells. As a result, the heart undergoes failure and potentially lethal arrhythmias. It is still a major reason for drug failure in preclinical and clinical phases of drug discovery. Current methods for predicting cardiotoxicity are based on guidelines that combine electrophysiological analysis of cell lines expressing ion channels ectopically in vitro with animal models and clinical trials. Although no new cases of drugs linked to lethal arrhythmias have been reported since the introduction of these guidelines in 2005, their limited predictive power likely means that potentially valuable drugs may not reach clinical practice. Human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) are now emerging as potentially more predictive alternatives, particularly for the early phases of preclinical research. However, these cells are phenotypically immature and culture and assay methods not standardized, which could be a hurdle to the development of predictive computational models and their implementation into the drug discovery pipeline, in contrast to the ambitions of the comprehensive pro-arrhythmia in vitro assay (CiPA) initiative. Here, we review present and future preclinical cardiotoxicity screening and suggest possible hPSC-CM-based strategies that may help to move the field forward. Coordinated efforts by basic scientists, companies and hPSC banks to standardize experimental conditions for generating reliable and reproducible safety indices will be helpful not only for cardiotoxicity prediction but also for precision medicine. Linked Articles: This article is part of a themed section on New Insights into Cardiotoxicity Caused by Chemotherapeutic Agents. To view the other articles in this section visit http://onlinelibrary.wiley.com/doi/10.1111/bph.v174.21/issuetoc.