Personal thermal management (PTM) is a technique leveraging advanced textile design to control the heat exchange between the human body and the external environment, thereby regulating microenvironments surrounding individuals and ensuring optimal thermal comfort. Critical to the PTM is heat conductivity, which serves as the primary mode of thermal transfer in textiles. Various materials with engineered thermal conductivities have been developed and incorporated into textiles for modulating warming and cooling effects toward achieving the optimal thermal comfort. However, the performance of reported textiles remains far from being satisfactory to meet the needs of daily use, especially in terms of heat management, wearability, and operational stability. Here, we first introduce mechanistic models for predicting the textiles’ thermal conductivity. Then, we provide a comprehensive overview of recent advancements in the design and realization of both single-function textiles (warming or cooling) and bifunctional textiles (switchable warming and cooling) based on mechanical force and various stimuli-responsive materials. We also analyze the major scientific and technological challenges for materializing the potential of textiles into practical applications in the PTM. Finally, an outlook is made on the future developments of the heat-conducting textiles and on the emerging applications of PTM technology.