Clinicians spend a large amount of time on clinical documentation of patient encounters, often impacting quality of care and clinician satisfaction, and causing physician burnout. Advances in artificial intelligence (AI) and machine learning (ML) open the possibility of automating clinical documentation with digital scribes, using speech recognition to eliminate manual documentation by clinicians or medical scribes. However, developing a digital scribe is fraught with problems due to the complex nature of clinical environments and clinical conversations. This paper identifies and discusses major challenges associated with developing automated speech-based documentation in clinical settings: recording high-quality audio, converting audio to transcripts using speech recognition, inducing topic structure from conversation data, extracting medical concepts, generating clinically meaningful summaries of conversations, and obtaining clinical data for AI and ML algorithms.