Smart healthcare has achieved significant progress in recent years. Emerging artificial intelligence (AI) technologies enable various smart applications across various healthcare scenarios. As an essential technology powered by AI, natural language processing (NLP) plays a key role in smart healthcare due to its capability of analysing and understanding human language. In this work, we review existing studies that concern NLP for smart healthcare from the perspectives of technique and application. We first elaborate on different NLP approaches and the NLP pipeline for smart healthcare from the technical point of view. Then, in the context of smart healthcare applications employing NLP techniques, we introduce representative smart healthcare scenarios, including clinical practice, hospital management, personal care, public health, and drug development. We further discuss two specific medical issues, i.e., the coronavirus disease 2019 (COVID-19) pandemic and mental health, in which NLP-driven smart healthcare plays an important role. Finally, we discuss the limitations of current works and identify the directions for future works.