Research in machine-learning (ML) algorithms using natural behavior (i.e., text, audio, and video data) suggests that these techniques could contribute to personalization in psychology and psychiatry. However, a systematic review of the current state-of-the-art is missing. Moreover, individual studies often target ML experts, and may overlook potential clinical implications of their findings. In a narrative accessible to mental health professionals, we present a systematic review, conducted in 5 psychology and 2 computer-science databases. We included 128 studies assessing the predictive power of ML algorithms using text, audio, and/or video data in the prediction of anxiety and post-traumatic stress (PTSD). Most studies (n = 87) aimed at predicting anxiety, the remainder (n = 41) focused on PTSD. They were mostly published since 2019, in computer science journals, and tested algorithms using text (n = 72), as opposed to audio or video. They focused mainly on general populations (n = 92), less on laboratory experiments (n = 23) or clinical populations (n = 13). Methodological quality varied, as did reported metrics of the predictive power, hampering comparison across studies. Two thirds of studies, focusing on both disorders, reported acceptable to very good predictive power (including high-quality studies only). Results of 33 studies were uninterpretable, mainly due to missing information. Research into ML algorithms using natural behavior is in its infancy, but shows potential to contribute to diagnostics of mental disorders, such as anxiety and PTSD, in the future, if standardization of methods, reporting of results, and research in clinical populations are improved.