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This review investigates the expanding influence of machine learning and deep learning methodologies within the healthcare sector, concentrating specifically on the vital challenges of interpretability and explainability inherent in black-box models. Although machine learning frameworks are increasingly deployed to assist in medical analytics and diagnostics, their intricate nature emphasizes the necessity of comprehending how these systems process and interpret data to facilitate well-informed clinical choices. This paper offers a thorough examination of the obstacles and potential solutions documented in existing scholarship, delivering a synthesis of contemporary techniques in this domain. Furthermore, it establishes precise conceptual boundaries for interpretability and explainability, seeking to untangle the differences between these notions and outline their consequences for clinical decision-making. Utilizing a dataset of 448 publications to address seven distinct research questions, our investigation demonstrates that this research area has experienced exponential growth over the past ten years. Additionally, the psychological factors governing public opinion highlight the vital need for transparent communication regarding the capabilities and constraints of artificial intelligence. To mitigate opacity, investigators are actively engineering strategies to lower model complexity and implement visual explanation tools. Nevertheless, maintaining a delicate equilibrium between high predictive performance and adequate model interpretability remains an ongoing challenge. Given the expanding role of artificial intelligence in supporting clinical diagnostics and therapeutics, the development of inherently interpretable artificial intelligence systems is critical. Within this rapidly changing paradigm, a steadfast dedication to transparency, ethical standards, and cross-disciplinary partnerships is essential to guarantee the conscientious deployment of artificial intelligence. This shared dedication is foundational to cementing long-term trust between medical professionals and patients, resolving novel problems, and promoting the educated integration of these sophisticated technologies into medical practices.