This paper presents a comprehensive study of Convolutional Neural Networks (CNN) and transfer learning in the context of medical imaging. Medical imaging plays a critical role in the diagnosis and treatment of diseases, and CNN-based models have demonstrated significant improvements in image analysis and classification tasks. Transfer learning, which involves reusing pre-trained CNN models, has also shown promise in addressing challenges related to small datasets and limited computational resources. This paper reviews the advantages of CNN and transfer learning in medical imaging, including improved accuracy, reduced time and resource requirements, and the ability to address class imbalances. It also discusses challenges, such as the need for large and diverse datasets, and the limited interpretability of deep learning models. What factors contribute to the success of these networks? How are they fashioned, exactly? What motivated them to build the structures that they did? Finally, the paper presents current and future research directions and opportunities, including the development of specialized architectures and the exploration of new modalities and applications for medical imaging using CNN and transfer learning techniques. Overall, the paper highlights the significant potential of CNN and transfer learning in the field of medical imaging, while also acknowledging the need for continued research and development to overcome existing challenges and limitations.