Suicide poses a significant threat to global public health and well-being. Identifying suicidal tendencies and intervening in advance are effective means of suicide prevention. With the rapid popularity of social media, it has become a platform for people to express their opinions and share their statuses, making it possible to develop identification technology for suicidal tendencies based on social media. From the perspectives of cognitive linguistics and psychology, we have examined research directions and technical methods, sorting out the advantages and disadvantages of recent suicidal tendency identification technology and conducting a comparative analysis. We have further subdivided the task of suicidal tendency recognition in more detail, discussed the developmental trends of suicidal tendency recognition, and proposed possible future research directions. Simultaneously, we have summarized relevant datasets and other resources for the reference of researchers.