Heart disease remains one of the leading causes of death in industrialized nations with myocardial infarction (MI) contributing to at least one fifth of the reported deaths. The hypoxic environment eventually leads to cellular death and scar tissue formation. The scar tissue that forms is not mechanically functional and often leads to myocardial remodeling and eventual heart failure. Tissue engineering and regenerative medicine principles provide an alternative approach to restoring myocardial function by designing constructs that will restore the mechanical function of the heart. In this review, we will describe the cellular events that take place after an MI and describe current treatments. We will also describe how biomaterials, alone or in combination with a cellular component, have been used to engineer suitable myocardium replacement constructs and how new advanced culture systems will be required to achieve clinical success.