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With the emergence of an increasing number of functional near-infrared spectroscopy (fNIRS) devices, the significant deterioration in measurement caused by motion artifacts has become an essential research topic for fNIRS applications. However, a high requirement for mathematics and programming limits the number of related researches. Therefore, here we provide the first comprehensive review for motion artifact removal in fNIRS aiming to (i) summarize the latest achievements, (ii) present the significant solutions and evaluation metrics from the perspective of application and reproduction, and (iii) predict future topics in the field. The present review synthesizes information from fifty-one journal articles (screened according to three criteria). Three hardware-based solutions and nine algorithmic solutions are summarized, and their application requirements (compatible signal types, the availability for online applications, and limitations) and extensions are discussed. Five metrics for noise suppression and two metrics for signal distortion were synthesized to evaluate the motion artifact removal methods. Moreover, we highlight three deficiencies in the existing research: (i) The balance between the use of auxiliary hardware and that of an algorithmic solution is not clarified; (ii) few studies mention the filtering delay of the solutions, and (iii) the robustness and stability of the solution under extreme application conditions are not discussed. [ABSTRACT FROM AUTHOR]