Anxiety disorder (AD) is a major mental health illness. However, due to the many symptoms and confounding factors associated with AD, it is difficult to diagnose, and patients remain untreated for a long time. Therefore, researchers have become increasingly interested in non-invasive biosignals, such as electroencephalography (EEG), electrocardiogram (ECG), electrodermal response (EDA), and respiration (RSP). Applying machine learning to these signals enables clinicians to recognize patterns of anxiety and differentiate a sick patient from a healthy one. Further, models with multiple and diverse biosignals have been developed to improve accuracy and convenience. This paper reviews and summarizes studies published from 2012 to 2022 that applied different machine learning algorithms with various biosignals. In doing so, it offers perspectives on the strengths and weaknesses of current developments to guide future advancements in anxiety detection. Specifically, this literature review reveals promising measurement accuracies ranging from 55% to 98% for studies with sample sizes of 10 to 102 participants. On average, studies using only EEG seemed to obtain the best performance, but the most accurate results were obtained with EDA, RSP, and heart rate. Random forest and support vector machines were found to be widely used machine learning methods, and they lead to good results as long as feature selection has been performed. Neural networks are also extensively used and provide good accuracy, with the benefit that no feature selection is needed. This review also comments on the effective combinations of modalities and the success of different models for detecting anxiety.