Creating descriptive text from medical images to aid in diagnosis and treatment planning is known as medical image captioning, and it is a crucial duty in the healthcare industry. In this study, medical image captioning techniques are systematically reviewed in the literature with an emphasis on Transformer-based models and Convolutional Neural Network-Long Short Term Memory (CNN-LSTM). Aspects like as model designs, datasets, evaluation measures, and difficulties encountered in practical implementations are all examined in this paper. According to the results, Transformer-based models, specifically Swin Transformer and Vision Transformer (ViT), perform better than CNN-LSTM-based models in terms of BLEU, ROUGE, CIDEr, and METEOR scores, resulting in more accurate clinically relevant caption generation. However, there are still a number of issues, including interpretability, computing requirements, and data restrictions. Potential future routes to increase the efficacy and practical application of medical image captioning systems are covered in this paper, including hybrid model approaches, data augmentation techniques, and enhanced explainability methodologies.