The number of clinician burnouts is increasing and has been linked to a high administrative burden. Automatic speech recognition (ASR) and natural language processing (NLP) techniques may address this issue by creating the possibility of automating clinical documentation with a "digital scribe". We reviewed the current status of the digital scribe in development towards clinical practice and present a scope for future research. We performed a literature search of four scientific databases (Medline, Web of Science, ACL, and Arxiv) and requested several companies that offer digital scribes to provide performance data. We included articles that described the use of models on clinical conversational data, either automatically or manually transcribed, to automate clinical documentation. Of 20 included articles, three described ASR models for clinical conversations. The other 17 articles presented models for entity extraction, classification, or summarization of clinical conversations. Two studies examined the system's clinical validity and usability, while the other 18 studies only assessed their model's technical validity on the specific NLP task. One company provided performance data. The most promising models use context-sensitive word embeddings in combination with attention-based neural networks. However, the studies on digital scribes only focus on technical validity, while companies offering digital scribes do not publish information on any of the research phases. Future research should focus on more extensive reporting, iteratively studying technical validity and clinical validity and usability, and investigating the clinical utility of digital scribes.