The global mortality rate is known to be the highest due to cardiovascular disease (CVD). Thus, preventive, and early CVD risk identification in a non-invasive manner is vital as healthcare cost is increasing day by day. Conventional methods for risk prediction of CVD lack robustness due to the non-linear relationship between risk factors and cardiovascular events in multi-ethnic cohorts. Few recently proposed machine learning-based risk stratification reviews without deep learning (DL) integration. The proposed study focuses on CVD risk stratification by the use of techniques mainly solo deep learning (SDL) and hybrid deep learning (HDL). Using a PRISMA model, 286 DL-based CVD studies were selected and analyzed. The databases included were Science Direct, IEEE Xplore, PubMed, and Google Scholar. This review is focused on different SDL and HDL architectures, their characteristics, applications, scientific and clinical validation, along with plaque tissue characterization for CVD/stroke risk stratification. Since signal processing methods are also crucial, the study further briefly presented Electrocardiogram (ECG)-based solutions. Finally, the study presented the risk due to bias in AI systems. The risk of bias tools used were (I) ranking method (RBS), (II) region-based map (RBM), (III) radial bias area (RBA), (IV) prediction model risk of bias assessment tool (PROBAST), and (V) risk of bias in non-randomized studies-of interventions (ROBINS-I). The surrogate carotid ultrasound image was mostly used in the UNet-based DL framework for arterial wall segmentation. Ground truth (GT) selection is vital for reducing the risk of bias (RoB) for CVD risk stratification. It was observed that the convolutional neural network (CNN) algorithms were widely used since the feature extraction process was automated. The ensemble-based DL techniques for risk stratification in CVD are likely to supersede the SDL and HDL paradigms. Due to the reliability, high accuracy, and faster execution on dedicated hardware, these DL methods for CVD risk assessment are powerful and promising. The risk of bias in DL methods can be best reduced by considering multicentre data collection and clinical evaluation.