Natural gas hydrates are ice-like mixtures of gas (mostly methane) and water that are widely found in sediments along the world’s continental margins and within and beneath permafrost in a near-surface depth interval where the pressure is sufficiently high and temperature sufficiently low for gas hydrate to be stable. Beneath this interval, gas hydrate is not stable and free gas may be present. This paper reviews the multiple quantitative models that have proposed to describe the genesis of gas hydrate in geological systems. We emphasize the importance of coupling multi-phase flow (vapor and liquid) and multicomponent reactive transport with geological history to describe the dynamical processes of gas hydrate formation and evolution in geological systems. By understanding the generation and evolution of gas hydrate through time, we will better understand their role in the carbon cycle, their potential to contribute to climate change and geohazards, and how to design optimal strategies for the environmentally safe production of gas from hydrate reservoirs.