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With the rapid development of smart grids and distributed energy sources, the home energy management system (HEMS) is becoming a hot topic of research as a hub for connecting customers and utilities for energy visualization. Accurate forecasting of future short-term residential electricity demand for each major appliance is a key part of the energy management system. This paper aims to explore the current research status of household-level short-term load forecasting, summarize the advantages and disadvantages of various forecasting methods, and provide research ideas for short-term household load forecasting and household energy management. Firstly, the paper analyzes the latest research results and research trends in deep learning load forecasting methods in terms of network models, feature extraction, and adaptive learning; secondly, it points out the importance of combining probabilistic forecasting methods that take into account load uncertainty with deep learning techniques; and further explores the implications and methods for device-level as well as ultra-short-term load forecasting. In addition, the paper also analyzes the importance of short-term household load forecasting for the scheduling of electricity consumption in household energy management systems. Finally, the paper points out the problems in the current research and proposes suggestions for future development of short-term household load forecasting. [ABSTRACT FROM AUTHOR]