Understanding human mobility behaviours is critical to improving operation efficiency, individual and organisational productivity, public health management, and quality of life in cities. Recent Generative AI approaches and Large Language Models (LLMs) has become a compelling choice for modelling mobility behaviours, especially in cases when training data is limited. I will present generalisable spatiotemporal and trajectory modeling approaches with Transformer-based architecture, which underpins current foundational AI and LLMs, for mobility modelling. I will also briefly present our works done in the last three years on leveraging Large Language Models (LLMs) for time-series forecasting and human mobility prediction using natural language prompts.