Intelligent algorithms can empower the development of smart manufacturing, since they can provide optimal solutions for detection, analysis, prediction and optimization. In recent ten years, publications on intelligent algorithms in smart manufacturing have increased sharply, showing superior performance in solving problems such as shop-floor scheduling, equipment prognosis, product defect detection and manufacturing service composition, etc. In this context, this paper focuses on the selection of commonly used top ten algorithms by providing a sound understanding of how they contribute to improving manufacturing processes. First, it presents a comprehensive survey and bibliometric analysis according to relevant literature. On this basis, the top ten algorithms are highlighted and reviewed. Then three key issues concerning when to use these algorithms in smart manufacturing, how to use them, as well as why to use them are studied. Finally, the challenges for the ten algorithms are summarized.