Brain wave signal is a bioelectric phenomenon reflecting activities in human brain. In this paper, we firstly introduce brain wave-based identity recognition techniques and the state-of-the-art work. We then analyze important features of brain wave and present challenges confronted by its applications. Further, we evaluate the security and practicality of using brain wave in identity recognition and anticounterfeiting authentication and describe use cases of several machine learning methods in brain wave signal processing. Afterwards, we survey the critical issues of characteristic extraction, classification, and selection involved in brain wave signal processing. Finally, we propose several brain wave-based identity recognition techniques for further studies and conclude this paper.