The detection of cardiac biomarkers is used for diagnostics, prognostics, and the risk assessment of cardiovascular diseases. The analysis of cardiac biomarkers is routinely performed with high-sensitivity immunological assays. Aptamers offer an attractive alternative to antibodies for analytical applications but, to date, are not widely practically implemented in diagnostics and medicinal research. This review summarizes the information on the most common cardiac biomarkers and the current state of aptamer research regarding these biomarkers. Aptamers as an analytical tool are well established for troponin I, troponin T, myoglobin, and C-reactive protein. For the rest of the considered cardiac biomarkers, the isolation of novel aptamers or more detailed characterization of the known aptamers are required. More attention should be addressed to the development of dual-aptamer sandwich detection assays and to the studies of aptamer sensing in alternative biological fluids. The universalization of aptamer-based biomarker detection platforms and the integration of aptamer-based sensing to clinical studies are demanded for the practical implementation of aptamers to routine diagnostics. Nevertheless, the wide usage of aptamers for the diagnostics of cardiovascular diseases is promising for the future, with respect to both point-of-care and laboratory testing.