Everyday thousands of cardiac surgeries are performed worldwide. This article reviews numerous studies on the use of Convolutional Neural Networks and their impact on vascular surgery. The development of computer systems supported by convolutional neural networks that contribute to vascular surgeries represents an important deviation from traditional approaches to the performance of surgical interventions, either through computed tomography verification or the method in which a surgeon ceases to participate in this type of surgical interventions. A systematic literature review (SLR) regarding convolutional neural networks for use in vascular surgeries was conducted for research from 2016 to 2021. The search strategy identified 15,505 papers from various search sources such as ACM Digital Library, EBSCOhost, Google Scholar, IEEE Xplore, MDPI, Microsoft Academic, ProQuest, ScienceDirect, Scopus, Springer, Web of Science, and Wiley Online Library, from which only 70 papers were considered (selected) based on exclusion criteria. The SLR focused on recent studies on convolutional neural networks where their use in vascular surgeries has been identified. This SLR provides readers with a mapping of all identified findings, making a comparison by relevance in regard to their own settings and possible scenarios. Therefore, it is hoped that this research will help other researchers to understand the current status of Convolutional Neural Networks and their application in Vascular Surgeries.