Deep learning (DL) is a branch of machine learning and artificial intelligence that has been applied to many areas in different domains such as health care and drug design. Cancer prognosis estimates the ultimate fate of a cancer subject and provides survival estimation of the subjects. An accurate and timely diagnostic and prognostic decision will greatly benefit cancer subjects. DL has emerged as a technology of choice due to the availability of high computational resources. The main components in a standard computer-aided design (CAD) system are preprocessing, feature recognition, extraction and selection, categorization, and performance assessment. Reduction of costs associated with sequencing systems offers a myriad of opportunities for building precise models for cancer diagnosis and prognosis prediction. In this survey, we provided a summary of current works where DL has helped to determine the best models for the cancer diagnosis and prognosis prediction tasks. DL is a generic model requiring minimal data manipulations and achieves better results while working with enormous volumes of data. Aims are to scrutinize the influence of DL systems using histopathology images, present a summary of state-of-the-art DL methods, and give directions to future researchers to refine the existing methods.