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 focus on feature extraction and modelling for various NLP tasks encountered in smart healthcare from a technical point of view. In the context of smart healthcare applications employing NLP techniques, the elaboration largely attends to representative smart healthcare scenarios, including clinical practice, hospital management, personal care, public health, and drug development. We further discuss the limitations of current works and identify the directions for future works.