Cardiac tissue engineering is very much in a current focus of regenerative medicine research as it represents a promising strategy for cardiac disease modelling, cardiotoxicity testing and cardiovascular repair. Advances in this field over the last two decades have enabled the generation of human engineered cardiac tissue constructs with progressively increased functional capabilities. However, reproducing tissue-like properties is still a pending issue, as constructs generated to date remain immature relative to native adult heart. Moreover, there is a high degree of heterogeneity in the methodologies used to assess the functionality and cardiac maturation state of engineered cardiac tissue constructs, which further complicates the comparison of constructs generated in different ways. Here, we present an overview of the general approaches developed to generate functional cardiac tissues, discussing the different cell sources, biomaterials, and types of engineering strategies utilized to date. Moreover, we discuss the main functional assays used to evaluate the cardiac maturation state of the constructs, both at the cellular and the tissue levels. We trust that researchers interested in developing engineered cardiac tissue constructs will find the information reviewed here useful. Furthermore, we believe that providing a unified framework for comparison will further the development of human engineered cardiac tissue constructs displaying the specific properties best suited for each particular application.