Medical vision-language models (VLMs) combine computer vision and natural language processing to analyze visual and textual medical data. Our paper reviews recent advancements in developing VLMs specialized for healthcare, focusing on models designed for medical report generation and visual question answering. We provide background on natural language processing and computer vision, explaining how techniques from both fields are integrated into VLMs to enable learning from multimodal data. Key areas we address include the exploration of medical vision-language datasets, in-depth analyses of architectures and pre-training strategies employed in recent noteworthy medical VLMs, and comprehensive discussion on evaluation metrics for assessing VLMs' performance in medical report generation and visual question answering. We also highlight current challenges and propose future directions, including enhancing clinical validity and addressing patient privacy concerns. Overall, our review summarizes recent progress in developing VLMs to harness multimodal medical data for improved healthcare applications.