Two-phase flow is a prevalent phenomenon encountered in engineering systems. In pipelines, the existence of two-phase flow introduces more intricate fluctuations in the excitation force compared to single-phase flow, leading to intensified vibrations known as Flow-Induced Vibration(FIV). FIV in pipelines with two-phase flow involves complex theoretical calculations, experiments, and simulations. This paper provides a comprehensive and detailed review of the internal gas-liquid two-phase FIV without phase change. It covers various aspects, including theoretical models, research methods, factors influencing FIV, factors influencing the dynamic response of pipes, and noise generated by internal two-phase flow. It presents the current frontiers of development in these fields, summarizes existing shortcomings, and outlines research prospects and future challenges. The latest research focuses on the construction of unsteady flow theoretical models, improving the tracking accuracy of phase interfaces, the application of VOF and two-fluid models in different flow patterns, and the application of machine learning. The primary challenge at present is to reduce the uncertainty in void fraction correlations and interphase relationship models; enhance the accuracy of phase interface simulations and effectively capture bubble dynamics in two-phase flow numerical models; and investigate the mechanisms of two-phase FIV coupled with external vortex-induced vibrations in long vertical pipes.