Liquefied natural gas is mostly stored and transported in cryogenic state in sizeable, costly, insulated, tanks of mainly cylindrical dimensions. These storage tanks are complex two-phase systems involving feed-product flows and flashing-recirculation flows. They are also substantially impacted by evaporation, condensation, heat leaks, and boil-off gas removal. These processes lead to state transients with significant mechanical, safety, environmental, and efficiency implications. Several dynamic simulation models were developed by researchers/companies worldwide, to gain practical and useful insights into boil-off gas removal and pressure management. These models are broadly classified into two broad categories. First are the simplified, fast, and inexpensive lumped parameter models, also used in several commercial process simulators. Second are the comprehensive, rigorous, and computationally expensive computational fluid dynamics (CFD) models. Additionally, there are practical and industrially useful models/simulators that capture the rigor of CFD models with less computational time and cost. This chapter provides an overview of the existing models in the literature and commercial simulators and describes their novelty, complexity, and usefulness in predicting the various state variables such as liquid level, temperature, pressure, and composition in a cryogenic tank.