Deep subsea facilities with high pressure and low temperature operation, encounter formation of gas hydrates as the most challenging problem in flow assurance. CSMHyK is a transient gas hydrate model specially designed for oil-dominated systems that predicts the formation and transportability of gas hydrates in flowlines. This paper presents a description of three sub-models included in the current version of CSMHyK: kinetics model, transport model and cold flow model; the product of intense efforts over a decade of hydrate research, involving over 20 students at the Center for Hydrate Research at the Colorado School of Mines. A set of conceptual pictures is also presented to describe physical phenomena of gas hydrate formation in water-dominated and gas-dominated systems, as the initial step of a development process that aims to extend CSMHyK towards a comprehensive model, to predict where and when hydrate plugs will form.