Cardiovascular disease (CVD) is the leading cause of death worldwide, casting a substantial economic footprint and burdening the global healthcare system. Historically, pre-clinical CVD modeling and therapeutic screening have been performed using animal models. Unfortunately, animal models oftentimes fail to adequately mimic human physiology, leading to a poor translation of therapeutics from pre-clinical trials to consumers. Even those that make it to market can be removed due to unforeseen side effects. As such, there exists a clinical, technological, and economical need for systems that faithfully capture human (patho)physiology for modeling CVD, assessing cardiotoxicity, and evaluating drug efficacy. Heart-on-a-chip (HoC) systems are a part of the broader organ-on-a-chip paradigm that leverages microfluidics, tissue engineering, microfabrication, electronics, and gene editing to create human-relevant models for studying disease, drug-induced side effects, and therapeutic efficacy. These compact systems can be capable of real-time measurements and on-demand characterization of tissue behavior and could revolutionize the drug development process. In this review, we highlight the key components that comprise a HoC system followed by a review of contemporary reports of their use in disease modeling, drug toxicity and efficacy assessment, and as part of multi-organ-on-a-chip platforms. We also discuss future perspectives and challenges facing the field, including a discussion on the role that standardization is expected to play in accelerating the widespread adoption of these platforms.