Deep learning has become a prominent computational modeling tool in the areas of computer vision and image processing in recent years. This research comprehensively analyzes the different deep-learning methods used for image-to-image translation and reconstruction in the natural and medical imaging domains. We examine the famous deep learning frameworks, such as convolutional neural networks and generative adversarial networks, and their variants, delving into the fundamental principles and difficulties of each. In the field of natural computer vision, we investigate the development and extension of various deep-learning generative models. In comparison, we investigate the possible applications of deep learning to generative medical imaging problems, including medical image translation, MRI reconstruction, and multi-contrast MRI synthesis. This thorough review provides scholars and practitioners in the areas of generative computer vision and medical imaging with useful insights for summarizing past works and getting insight into future research paths.