Conversational agent-based psychotherapy is a novel field of research. Its importance has rapidly increased in recent years due to the heightened demand for psychotherapy treatment options and a related demand for cost-effective, scalable, and low-threshold solutions to provide mental health support to the general population. This methodological literature review investigates the current state of research on the effectiveness and acceptance of chatbot and voice assistant-based psychotherapy approaches by focusing on used measurement methods and achieved study outcomes. Following the updated PRISMA guidelines for reporting systematic reviews 1432 publications are identified and reduced to a result set of 22 publications based on a rigorous screening process. Overall, the current state of research suggests that conversational agents might be an effective treatment option for people with depression and anxiety and show good acceptance by users. As there is a high heterogeneity of study designs, and methodologies, and a lack of randomized controlled trials with conventional treatment control groups, more research in the field is needed.