Foundation models (FMs) have emerged as a powerful paradigm, enabling a diverse range of data analytics and knowledge discovery tasks across scientific fields. Inspired by the success of FMs, particularly large language models, researchers have recently begun to explore spatio-temporal foundation models (STFMs) to improve adaptability and generalization across a wide spectrum of spatio-temporal (ST) tasks. Despite rapid progress, a systematic investigation of trajectory foundation models (TFMs), a crucial subclass of STFMs, is largely lacking. This tutorial addresses this gap by offering a comprehensive overview of recent advances in TFMs, including a taxonomy of existing methodologies and a critical analysis of their strengths and limitations. In addition, the tutorial highlights open challenges and outlines promising research directions to advance spatio-temporal general intelligence through the development of robust, responsible, and transferable TFMs.