Heart diseases cause over 17.9 million total deaths globally, making them the leading source of mortality. The aim of this review is to describe the characteristic mechanical, chemical and cellular properties of human cardiac tissue and how these properties can be mimicked in 3D bioprinted tissues. Furthermore, the authors review how current healthy cardiac models are being 3D bioprinted using extrusion-, laser- and inkjet-based printers. The review then discusses the pathologies of cardiac diseases and how bioprinting could be used to fabricate models to study these diseases and potentially find new drug targets for such diseases. Finally, the challenges and future directions of cardiac disease modeling using 3D bioprinting techniques are explored.