Growing electricity demand, the deployment of renewable energy sources and the widespread use of smart home appliances provide new opportunities for home energy management systems (HEMSs), which can be defined as systems that improve the overall energy production and consumption of residential buildings by controlling and scheduling the use of household equipment. By saving energy, reducing residential electricity costs, optimizing the utilization rate and reliability of utility companies' power systems, and reducing air pollution for society, HEMSs lead to an enhancement in the socioeconomic development of low-carbon economies. This review aims to systematically analyze and summarize the development trends and challenges of HEMSs in recent years. This paper reviews the development history of the HEMS architecture and discusses the characteristics of several major communication technologies in the current HEMS infrastructure. In addition, the common objectives and constraints related to scheduling optimization are classified, and several optimization methods in the literature, including various intelligent algorithms, have been introduced, compared, and critically analyzed. Furthermore, experimental studies and challenges in the real world are also summarized and recommendations are given. This paper reveals the trend from simple to complex in the architecture and functionality of HEMSs, discusses the challenges for future improvements in modeling and scheduling, and shows the development of various modeling and scheduling methods. Based on this review, researchers can gain a comprehensive understanding of current research trends in HEMSs and open up ideas for developing new modeling and scheduling approaches by gaining insight into the trade-offs between optimum solutions and computational complexity.INDEX TERMS Demand response, home appliances, home energy management system, optimization, renewable energy resources, smart grid.