a b s t r a c tThe increasing demand for electricity and the emergence of smart grids have presented new opportunities for home energy management systems (HEMS) in demand response markets. HEMS are demand response tools that shift and curtail demand to improve the energy consumption and production profile of a dwelling on behalf of a consumer. HEMS usually create optimal consumption and production schedules by considering multiple objectives such as energy costs, environmental concerns, load profiles, and consumer comfort.The existing literature has presented several methods, such as mathematical optimization, model predictive control, and heuristic control, for creating efficient operation schedules and for making good consumption and production decisions. However, the effectiveness of the methods in the existing literature can be difficult to compare due to diversity in modelling parameters, such as appliance models, timing parameters, and objectives.The present paper provides a comparative analysis of the literature on HEMS, with a focus on modelling approaches and their impact on HEMS operations and outcomes. In particular, we discuss a set of HEMS challenges such as forecast uncertainty, modelling device heterogeneity, multi-objective scheduling, computational limitations, timing considerations, and modelling consumer well-being.The presented work is organized to allow a reader to understand and compare the important considerations, approaches, nomenclature, and results in prominent and new literary works without delving deeply into each one.