Engineering functional cardiac tissues remains an ongoing significant challenge due to the complexity of the native environment. However, our growing understanding of key parameters of the in vivo cardiac microenvironment and our ability to replicate those parameters in vitro are resulting in the development of increasingly sophisticated models of engineered cardiac tissues (ECT). This review examines some of the most relevant parameters that may be applied in culture leading to higher fidelity cardiac tissue models. These include the biochemical composition of culture media and cardiac lineage specification, co-culture conditions, electrical and mechanical stimulation, and the application of hydrogels, various biomaterials, and scaffolds. The review will also summarize some of the recent functional human tissue models that have been developed for in vivo and in vitro applications. Ultimately, the creation of sophisticated ECT that replicate native structure and function will be instrumental in advancing cell-based therapeutics and in providing advanced models for drug discovery and testing.