Representation learning has offered a revolutionary learning paradigm for various AI domains. In this survey, we examine and review the problem of representation learning with the focus on heterogeneous networks, which consists of different types of vertices and relations. The goal of this problem is to automatically project objects, most commonly, vertices, in an input heterogeneous network into a latent embedding space such that both the structural and relational properties of the network can be encoded and preserved. The embeddings (representations) can be then used as the features to machine learning algorithms for addressing corresponding network tasks. To learn expressive embeddings, current research developments can fall into two major categories: shallow embedding learning and graph neural networks. After a thorough review of the existing literature, we identify several critical challenges that remain unaddressed and discuss future directions. Finally, we build the Heterogeneous Graph Benchmark to facilitate open research for this rapidly-developing topic.