Cardiac tissue engineering aims at creating contractile structures that can optimally reproduce the features of human cardiac tissue. These constructs are becoming valuable tools to model some of the cardiac functions, to set preclinical platforms for drug testing, or to alternatively be used as therapies for cardiac repair approaches. Most of the recent developments in cardiac tissue engineering have been made possible by important advances regarding the efficient generation of cardiac cells from pluripotent stem cells and the use of novel biomaterials and microfabrication methods. Different combinations of cells, biomaterials, scaffolds, and geometries are however possible, which results in different types of structures with gradual complexities and abilities to mimic the native cardiac tissue. Here, we intend to cover key aspects of tissue engineering applied to cardiology and the consequent development of cardiac organoids. This review presents various facets of the construction of human cardiac 3D constructs, from the choice of the components to their patterning, the final geometry of generated tissues, and the subsequent readouts and applications to model and treat cardiac diseases.