This article attempts to review papers on power assist rehabilitation robots, human motion intention, control laws, and estimation of power assist rehabilitation robots based on human motion intention in recent years. This paper presents the various ways in which human motion intention in rehabilitation can be estimated. This paper also elaborates on the control laws for the estimation of motion intention of the power assist rehabilitation robot. From the review, it has been found that the motion intention estimation method includes: Artificial Intelligence-based motion intention and Model-based motion intention estimation. The controllers include hybrid force/position control, EMG control, and adaptive control. Furthermore, Artificial Intelligence based motion intention estimation can be subdivided into Electromyography (EMG), Surface Electromyography (SEMG), Extreme Learning Machine (ELM), and Electromyography-based Admittance Control (EAC). Also, Model-based motion intention estimation can be subdivided into Impedance and Admittance control interaction. Having reviewed several papers, EAC and ELM are proposed for efficient motion intention estimation under artificial-based motion intention. In future works, Impedance and Admittance control methods are suggested under model-based motion intention for efficient estimation of motion intention of power assist rehabilitation robot. In addition, hybrid force/position control and adaptive control are suggested for the selection of control laws. The findings of this review paper can be used for developing an efficient power assist rehabilitation robot with motion intention to aid people with lower or upper limb impairment.