Drugs can affect the cardiovascular (CV) system either as an intended treatment or as an unwanted side effect. In both cases, drug-induced cardiotoxicities such as arrhythmia and unfavourable hemodynamic effects can occur, and be described using mathematical models; such a model informed approach can provide valuable information during drug development and can aid decision-making. However, in order to develop informative models, it is vital to understand CV physiology. The aims of this tutorial are to present (1) key background biological and medical aspects of the CV system, (2) CV electrophysiology, (3) CV safety concepts, (4) practical aspects of development of CV models and (5) regulatory expectations with a focus on using model informed and quantitative approaches to support nonclinical and clinical drug development. In addition, we share several case studies to provide practical information on project strategy (planning, key questions, assumptions setting, and experimental design) and mathematical models development that support decision-making during drug discovery and development.