In the fifth-generation (5G) wireless communications system, various service requirements under different communication environments are expected to be satisfied. As a new evolution network structure, heterogeneous networks (HetNet) have been fully studied in recent years. In contrast to conventional homogeneous networks, the key feature of HetNet is to increase the opportunity of spatial resource reuse and improve the quality of service of users by allowing small cells to cooperate in macrocell networks. However, since the mutual interference among different users and the limited resource are existing in HetNets, efficient resource allocation (RA) schemes are very important to reduce the interference and achieve spectrum sharing. In this paper, we provide a comprehensive survey on RA in HetNets for 5G communications. Specifically, we first introduce the definition and different network scenarios of HetNet. Second, RA models are discussed. Then, we present classification to analyze current RA schemes in the existing references. Finally, some challenging open issues and future research trends are addressed in this field. We also provide two effective approaches for the sixth-generation (6G) communications to solve the RA problems of future Het-Nets, namely, a learning-based approach and a control theorybased approach. This paper provides important information on HetNets, which can be used to guide the development of more efficient RA schemes in this area.