The field of location prediction and trajectory analysis is witnessing significant advancements with the integration of large language models (LLMs) and innovative architectures. Researchers are addressing the challenges associated with applying LLMs to complex spatiotemporal tasks by leveraging tailored collaborative agents and dual-level Mixture-of-Experts (MoE) designs. These approaches have shown promising results in capturing the complex semantics of real-world locations and modeling heterogeneous behavioral dynamics across diverse user groups. Additionally, there is a growing interest in learning lightweight embeddings for short trajectories, enabling efficient and interpretable motion forecasting pipelines. Noteworthy papers in this area include CoMaPOI, which pioneers the investigation of challenges associated with applying LLMs to complex spatiotemporal tasks, and NextLocMoE, which achieves superior performance in terms of predictive accuracy, cross-domain generalization, and interpretability. Furthermore, the Contrast & Compress framework demonstrates the effectiveness of learning fixed-dimensional embeddings for short trajectories using a Transformer encoder trained with a contrastive triplet loss. Overall, these developments are pushing the boundaries of location prediction and trajectory analysis, enabling more accurate and efficient modeling of human mobility patterns.