Understanding the behavior of materials at extreme pressures is a central issue in fields like aerodynamics, astronomy, and geology, as well as for advancing technological grand challenges such as inertial confinement fusion. Dynamic compression experiments to probe high-pressure states often encounter rapid phase transitions that may cause the materials to behave in unexpected ways, and understanding the kinetics of these phase transitions remains an area of great interest. In this review, we examine experimental and theoretical/computational efforts to study the freezing kinetics of water to a high-pressure solid phase known as ice VII. We first present a detailed analysis of dynamic compression experiments in which water has been observed to freeze on sub-microsecond time scales to ice VII. This is followed by a discussion of the limitations of currently available molecular and continuum simulation methods in modeling these experiments. We then describe how our phase transition kinetics models, which are based on classical nucleation theory, provide a more physics-based framework that overcomes some of these limitations. Finally, we give suggestions on future experimental and modeling work on the liquid-ice VII transition, including an outline of the development of a predictive multiscale model in which molecular and continuum simulations are intimately coupled.