The paradigm of Industry 5.0 pushes the transition from the traditional to a novel, smart, digital, and connected industry, where well-being is key to enhance productivity, optimize man-machine interaction and guarantee workers' safety. This work aims to conduct a systematic review of current methodologies for monitoring and analyzing physical and cognitive ergonomics. Three research questions are addressed: (1) which technologies are used to assess the physical and cognitive well-being of workers in the workplace, (2) how the acquired data are processed, and (3) what purpose this well-being is evaluated for. This way, individual factors within the holistic assessment of worker well-being are highlighted, and information is provided synthetically. The analysis was conducted following the PRISMA 2020 statement guidelines. From the sixty-five articles collected, the most adopted (1) technological solutions, (2) parameters, and (3) data analysis and processing were identified. Wearable inertial measurement units and RGB-D cameras are the most prevalent devices used for physical monitoring; in the cognitive ergonomics, and cardiac activity is the most adopted physiological parameter. Furthermore, insights on practical issues and future developments are provided. Future research should focus on developing multi-modal systems that combine these aspects with particular emphasis on their practical application in real industrial settings.