Standard named entity recognizers can effectively recognize entity mentions that consist of contiguous tokens and do not overlap with each other. However, in practice, there are many domains, such as the biomedical domain, in which there are nested, overlapping, and discontinuous entity mentions. These complex mentions cannot be directly recognized by conventional sequence tagging models because they may break the assumptions based on which sequence tagging techniques are built. We review the existing methods which are revised to tackle complex entity mentions and categorize them as tokenlevel and sentence-level approaches. We then identify the research gap, and discuss some directions that we are exploring.