Smart manufacturing aims to create highly customizable products with higher quality and lower costs by integrating Industrial Internet of Things, big data analytics, cloud computing, and advanced robots into factory floors. As manufacturing equipment and devices have been increasingly equipped with sensors as well as connected via wireless network or wired Ethernet, smart manufacturing systems are becoming more accessible than ever through the Internet. While advancement in sensing, artificial intelligence, and wireless technologies enables a paradigm shift in manufacturing, cyber-attacks pose a significant threat to the manufacturing sector. The objective of this paper is to review and discuss state-of-the-art technologies that can address cyber security issues in smart manufacturing. Specifically, vulnerability assessment and cyber attacks (e.g., man-in-the-middle and denial-of-service) are presented. Existing strategies that mitigate targeted cyber intrusions are also discussed. In addition, research gaps and challenges are identified to improve cyber security in critical manufacturing industries.