In recent years, cardiovascular diseases (CVDs) have become one of the leading causes of mortality globally. At early stages, CVDs appear with minor symptoms and progressively get worse. The majority of people experience symptoms such as exhaustion, shortness of breath, ankle swelling, fluid retention, and other symptoms when starting CVD. Coronary artery disease (CAD), arrhythmia, cardiomyopathy, congenital heart defect (CHD), mitral regurgitation, and angina are the most common CVDs. Clinical methods such as blood tests, electrocardiography (ECG) signals, and medical imaging are the most effective methods used for the detection of CVDs. Among the diagnostic methods, cardiac magnetic resonance imaging (CMRI) is increasingly used to diagnose, monitor the disease, plan treatment and predict CVDs. Coupled with all the advantages of CMR data, CVDs diagnosis is challenging for physicians as each scan has many slices of data, and the contrast of it might be low. To address these issues, deep learning (DL) techniques have been employed in the diagnosis of CVDs using CMR data, and much research is currently being conducted in this field. This review provides an overview of the studies performed in CVDs detection using CMR images and DL techniques. The introduction section examined CVDs types, diagnostic methods, and the most important medical imaging techniques. The following presents research to detect CVDs using CMR images and the most significant DL methods. Another section discussed the challenges in diagnosing CVDs from CMRI data. Next, the discussion section discusses the results of this review, and future work in CVDs diagnosis from CMR images and DL techniques are outlined. Finally, the most important findings of this study are presented in the conclusion section.