Real-world complex networks are inherently heterogeneous; they have different types of nodes, attributes, and relationships. In recent years, various methods have been proposed to automatically learn how to encode the structural and semantic information contained in heterogeneous information networks (HINs) into low-dimensional embeddings; this task is called heterogeneous network embedding (HNE). Efficient HNE techniques can benefit various HIN-based machine learning tasks such as node classification, recommender systems, and information retrieval. Here, we provide a comprehensive survey of key advancements in the area of HNE. First, we define an encoder-decoder-based HNE model taxonomy. Then, we systematically overview, compare, and summarize various state-of-the-art HNE models and analyze the advantages and disadvantages of various model categories to identify more potentially competitive HNE frameworks. We also summarize the application fields, benchmark datasets, open source tools, and performance evaluation in the HNE area. Finally, we discuss open issues and suggest promising future directions. We anticipate that this survey will provide deep insights into research in the field of HNE.