Deep learning algorithms have become the first choice as an approach to medical image analysis, face recognition, and emotion recognition. In this survey, several deep-learning-based approaches applied to breast cancer, cervical cancer, brain tumor, colon and lung cancers are studied and reviewed. Deep learning has been applied in almost all of the imaging modalities used for cervical and breast cancers and MRIs for the brain tumor. The result of the review process indicated that deep learning methods have achieved state-of-the-art in tumor detection, segmentation, feature extraction and classification. As presented in this paper, the deep learning approaches were used in three different modes that include training from scratch, transfer learning through freezing some layers of the deep learning network and modifying the architecture to reduce the number of parameters existing in the network. Moreover, the application of deep learning to imaging devices for the detection of various cancer cases has been studied by researchers affiliated to academic and medical institutes in economically developed countries; while, the study has not had much attention in Africa despite the dramatic soar of cancer risks in the continent.