Human behavior, despite its complexity, follows structured principles. Better understanding the underlying concepts of human behavior in an industrial setting can help us to create more reliable and effective collaborative robotic environments. In factories, robots can interact with humans in unseen situations through sensing, processing, and predicting human behaviors. This work summarizes the efforts to express human behavior in industrial human-robot interactions (HRI) in manufacturing. For this purpose, all papers related to HRI in production systems, additive manufacturing, agent behavior, human cognition, cloud robotics, cooperative Markov decision process, multi-robot design, and collaborative robots are reviewed in this work. The discussion includes the existing methods, research gaps, and future research directions for envisioning a safer yet more efficient HRI practice. In detail, we discuss current research about human-centered HRI and robot-centered HRI based on the focus areas such as factorial analysis, predictive analysis, and control structures for social and/or industrial/manufacturing robots. In the last part, based on our findings, we report major limitations of the existing literature and propose future research directions such as cognitive modeling, perception development, interaction design, sensor-based control, and social effects in manufacturing.