Psychiatric disorders exhibit extremely high heterogeneity, thus making accurate diagnosis and timely treatment challenging. Numerous neuroimaging studies have revealed abnormal changes in brain functional connectivity among patients with psychiatric disorders. To better understand the complexity of these disorders, researchers have explored hypergraph-based methods. Using functional magnetic resonance imaging data and hypergraph theory, studies have modeled and analyzed brain functional connectivity hypernetworks to classify psychiatric disorders and identify associated biomarkers. Furthermore, modeling a subjects-level hypergraph aids in estimating potential higher-order relationships among individuals; thus, hypergraphs can be used for classifying psychiatric disorders and identifying biomarkers. Recent neuroimaging studies have revealed specific subtypes of psychiatric disorders with biological importance. Hypergraph-based clustering methods have been used to investigate subtypes of psychiatric disorders. However, limited work has surveyed the applications of hypergraph-based methods in classifying and subtyping psychiatric disorders. To address this gap, this article provides a thorough survey, and discusses current challenges and potential future research directions in this field.