Artificial Intelligence (AI) has redefined the landscape of the healthcare sector by offering accurate diagnosis, analysis, and treatment of various diseases, amongst other benefits. Notably, most advanced AI systems are viewed as 'black boxes,' owing to the lack of transparency of decision-making processes, making it difficult for medical and healthcare experts to put their trust in AI. Explainability of Artificial Intelligence (XAI) seeks to remedy this challenge facing the medical and healthcare sector by offering insights into the decision-making of AI systems. In the paper, the author offers a comprehensive review of various Explainability of Artificial Intelligence systems in the medical and healthcare sector, amongst key disciplines like radiology, oncology, cardiology, and telemedicine, amongst various AI systems. According to the review, Explainability of Artificial Intelligence systems are of critical importance in the medical and healthcare sector, considering the evaluation of AI systems, for instance, in medical environments, where accuracy and explanations of AI decision-making processes are paramount for the sector.