The ever increasing demand for electricity and the rapid increase in the number of automatic electrical appliances have posed a critical energy management challenge for both utilities and consumers. Substantial work has been reported on the Home Energy Management System (HEMS) but to the best of our knowledge, there is no single review highlighting all recent and past developments on Demand Side Management (DSM) and HEMS altogether. The purpose of each study is to raise user comfort, load scheduling, energy minimization, or economic dispatch problem. Researchers have proposed different soft computing and optimization techniques to address the challenge, but still it seems to be a pressing issue. This paper presents a comprehensive review of research on DSM strategies to identify the challenging perspectives for future study. We have described DSM strategies, their deployment and communication technologies. The application of soft computing techniques such as Fuzzy Logic (FL), Artificial Neural Network (ANN), and Evolutionary Computation (EC) is discussed to deal with energy consumption minimization and scheduling problems. Different optimization-based DSM approaches are also reviewed. We have also reviewed the practical aspects of DSM implementation for smart energy management.