Electronic health record systems transformed healthcare documentation by providing a system for storing and sharing extensive patient data. However, much of this information remains in the form of unstructured text, which limits its utility for computational analysis. Natural Language Processing (NLP) has emerged as a prominent approach to extract and structure information from free-text clinical narratives, offering the potential to unlock valuable insights for clinical care, research, and administration. This paper provides an overview of recent advances in NLP methods applied to EHRs, discusses open problems including data quality, privacy, and generalizability, and highlights potential future directions for the integration of NLP into clinical workflows. The conclusions point to the need for continued development of domain-specific language models, privacy-preserving techniques, and explainable AI methods to fully harness the power of NLP for healthcare transformation.