Context: The academic community in Software Engineering (SE) has increasingly embraced Systematic Reviews (SRs) due to their numerous benefits. However, computational support for the SR process still needs improved to minimize the time and effort required for SR conduction. Objective: This study aims to identify the main computational solutions designed to support the conduction of SRs in SE. Method: A Systematic Mapping was carried out considering studies published from 2007 to May 2024 to answer the four research questions. Results: This study identified 38 computational approaches supporting SRs in SE, with the majority focusing on the conduction phase and implemented as tools or algorithms. Although research activity has grown recently, many solutions remain immature, with limited usability and integration. Key challenges include automation bias, search string construction, data management, and the lack of connective tools. Conclusion: The findings highlight the need for more integrated computational support across the SRs phases.