The world of technology is advancing by the day, presenting innovative and efficient solutions across various sectors, with healthcare being no exception. This review study majorly focuses on eliciting the impact of machine learning and deep learning techniques to improve the delivery of healthcare. It investigates the different frameworks of previous research studies to establish facts regarding the application of machine learning and deep learning, as well as where enhancement of the model is required. The strengths and weaknesses of the techniques used are identified. Our review study shows that the impact of machine learning and deep learning techniques cannot be berated, notably in prediction modelling, pattern recognition, classification, regression, and image processing, among other applications of the models. Furthermore, the study identifies numerous benefits of model explainability and different model explanation techniques, such as Alibi, InterpretML, Explainerdashboard, etc. We also show that prospective studies could employ ensemble learning using boosting and deep learning algorithms as core learning units.