<p>In Industry 4.0 and 5.0, human–robot interaction (HRI) is critical and common due to safety, reliability, high performance, and productivity speed up process while maintaining high productivity. The development in HRI systems led to further classifications such as human–robot collaboration (HRC) that is a fundamental principle in production environment. However, the implementations of HRC required critical considerations such as understanding the main aim of the collaborations, the movability, and dynamics in the working environment that specific types of controller model can be used and avoiding undesirable collisions with humans. Since selecting the accurate type of controller is essential for accomplishing the required accuracy with optimum performance and minimum error with handling complexity especially in delicate systems, this systematic review investigates and permits an intensive insight into impedance controller in HRI/HRC systems, with special focus on progress of variable impedance model, mainly by using fractional-order and fuzzy (<i>I</i> and <i>II</i>) methods. Besides, hybrid approaches in which learning-based methods are implemented are also highlighted. The differences between linear and nonlinear models are also pointed. Though, various industrial applications were discussed to emphasize the importance of cobots in innovation industries. It is observed that in dominant, the interaction force relying on impedance model was considered a linear structure with unknown coefficient whether the system is linear or nonlinear, and the adopted learning methods were only responsible to define the optimal (or near optimal) values of the linear components adopted in those models.</p>