There are many barriers to accessing mental health assessments including cost and stigma. Even when individuals receive professional care, assessments are intermittent and may be limited partly due to the episodic nature of psychiatric symptoms. Therefore, machine-learning technology using speech samples obtained in the clinic or remotely could one day be a biomarker to improve diagnosis and treatment. To date, reviews have only focused on using acoustic features from speech to detect depression and schizophrenia. Here, we present the first systematic review of studies using speech for automated assessments across a broader range of psychiatric disorders.