Dynamic software updating (DSU) is shifting gears to modify software systems without a halt. Even though extensive research has been conducted on DSU, it is necessary to synthesise and map the results of recent studies on DSU for prospective research highlights. This study aims to highlight the current state‐of‐the‐art, to recognise trends, and to identify existing open issues in DSU. A systematic mapping study (SMS) was conducted with a set of six research questions. A total of 1066 papers published from 2005 to 2019 were recorded. After a filtering process, 112 primary studies were selected and inspected. This study highlights the current state‐of‐the‐art of DSU including approaches, tools, models, and techniques. Also, this study outlines application domains, research type, and contributions type facets in DSU. In addition, this study demonstrates benchmarks, datasets, evaluation metrics, and existing open issues for future research in DSU. The results of this investigation can be used to highlight current state‐of‐the‐art of DSU, to show trends of DSU, and to demonstrate existing open issues in DSU.