Myocardial infarction is the most prevalent cardiovascular disease worldwide, and it is defined as cardiomyocyte cell death due to a lack of oxygen supply. Such a temporary absence of oxygen supply, or ischemia, leads to extensive cardiomyocyte cell death in the affected myocardium. Notably, reactive oxygen species are generated during the reperfusion process, driving a novel wave of cell death. Consequently, the inflammatory process starts, followed by fibrotic scar formation. Limiting inflammation and resolving the fibrotic scar are essential biological processes with respect to providing a favorable environment for cardiac regeneration that is only achieved in a limited number of species. Distinct inductive signals and transcriptional regulatory factors are key components that modulate cardiac injury and regeneration. Over the last decade, the impact of non-coding RNAs has begun to be addressed in many cellular and pathological processes including myocardial infarction and regeneration. Herein, we provide a state-of-the-art review of the current functional role of diverse non-coding RNAs, particularly microRNAs (miRNAs), long non-coding RNAs (lncRNAs), and circular RNAs (circRNAs), in different biological processes involved in cardiac injury as well as in distinct experimental models of cardiac regeneration.