Deep learning has brought about a significant transformation in machine learning, leading to an array of novel methodologies and consequently broadening its influence. The application of deep learning in various sectors, especially biomedical data analysis, has initiated a period filled with noteworthy scientific developments. This trend has majorly influenced cancer prognosis, where the interpretation of genomic data for survival analysis has become a central research focus. The capacity of deep learning to decode intricate patterns embedded within high-dimensional genomic data has provoked a paradigm shift in our understanding of cancer survival. Given the swift progression in this field, there is an urgent need for a comprehensive review that focuses on the most influential studies from 2021 to 2023. This review, through its careful selection and thorough exploration of dominant trends and methodologies, strives to fulfill this need. The paper aims to enhance our existing understanding of applications of deep learning in cancer survival analysis, while also highlighting promising directions for future research. This paper undertakes aims to enrich our existing grasp of the application of deep learning in cancer survival analysis, while concurrently shedding light on promising directions for future research in this vibrant and rapidly proliferating field.