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This paper reviews recent research on the demand flexibility of residential buildings in regard to definitions, flexible loads, and quantification methods. A systematic distinction of the terminology is made, including the demand flexibility, operation flexibility, and energy flexibility of buildings. A comprehensive definition of building demand flexibility is proposed based on an analysis of the existing definitions. Moreover, the flexibility capabilities and operation characteristics of the main residential flexible loads are summarized and compared. Models and evaluation indicators to quantify the flexibility of these flexible loads are reviewed and summarized. Current research gaps and challenges are identified and analyzed as well. The results indicate that previous studies have focused on the flexibility of central air conditioning, electric water heaters, wet appliances, refrigerators, and lighting, where the proportion of studies focusing on each of these subjects is 36.7%, 25.7%, 14.7%, 9.2%, and 8.3%, respectively. These flexible loads are different in running modes, usage frequencies, seasons, and capabilities for shedding, shifting, and modulation, while their response characteristics are not yet clear. Furthermore, recommendations are given for the application of white-, black-, and grey-box models for modeling flexible loads in different situations. Numerous static flexibility evaluation indicators that are based on the aspects of power, temporality, energy, efficiency, economics, and the environment have been proposed in previous publications, but a consensus and standardized evaluation framework is lacking. This review can help readers better understand building demand flexibility and learn about the characteristics of different residential flexible loads, while also providing suggestions for future research on the modeling techniques and evaluation metrics of residential building demand flexibility.