Mobility analysis is a crucial element in the research area of transportation systems. Forecasting traffic information offers a viable solution to address the conflict between increasing transportation demands and the limitations of transportation infrastructure. Predicting human travel is significant in aiding various transportation and urban management tasks, such as taxi dispatch and urban planning. Machine learning and deep learning methods are favored for their flexibility and accuracy. Nowadays, with the advent of large language models (LLMs), many researchers have combined these models with previous techniques or applied LLMs to directly predict future traffic information and human travel behaviors. However, there is a lack of comprehensive studies on how LLMs can contribute to this field. This survey explores existing approaches using LLMs for mobility forecasting problems. We provide a literature review concerning the forecasting applications within transportation systems, elucidating how researchers utilize LLMs, showcasing recent state-of-the-art advancements, and identifying the challenges that must be overcome to fully leverage LLMs in this domain.