In the domain of using DL-based methods in medical and healthcare prediction systems, the utilization of state-of-the-art deep learning (DL) methodologies assumes paramount significance. DL has attained remarkable achievements across diverse domains, rendering its efficacy particularly noteworthy in this context. The integration of DL with health and medical prediction systems enables real-time analysis of vast and intricate datasets, yielding insights that significantly enhance healthcare outcomes and operational efficiency in the industry. This comprehensive literature review systematically investigates the latest DL solutions for the challenges encountered in medical healthcare, with a specific emphasis on DL applications in the medical domain. By categorizing cutting-edge DL approaches into distinct categories, including convolutional neural networks (CNNs), recurrent neural networks (RNNs), generative adversarial networks (GANs), long short-term memory (LSTM) models, support vector machine (SVM), and hybrid models, this study delves into their underlying principles, merits, limitations, methodologies, simulation environments, and datasets. Notably, the majority of the scrutinized articles were published in 2022, underscoring the contemporaneous nature of the research. Moreover, this review accentuates the forefront advancements in DL techniques and their practical applications within the realm of medical prediction systems, while simultaneously addressing the challenges that hinder the widespread implementation of DL in image segmentation within the medical healthcare domains. These discerned insights serve as compelling impetuses for future studies aimed at the progressive advancement of using DL-based methods in medical and health prediction systems. The evaluation metrics employed across the reviewed articles encompass a broad spectrum of features, encompassing accuracy, precision, specificity, F-score, adoptability, adaptability, and scalability.