As ice-like crystals and non-stoichiometric compounds comprising gas and water, natural gas hydrates have drawn significant attention as a potential alternative energy source. This work focuses on holistically reviewing theoretical modeling and numerical studies conducted on the production of gas from natural gas hydrates. Firstly, fundamental models for the dissociation of a hydrate in a porous sediment are summarized in terms of the phase equilibrium and dissociation kinetics. The main features of different models and improvements for them are identified by clarifying crucial driving mechanisms and kinetic parameters. Subsequently, various numerical works addressing the dissociation of a hydrate in a porous sediment and the flow characteristics in a wellbore are reviewed, including aspects such as the theoretical background, computational scheme, and the physics involved. In general, profiting from a significant capacity to solve nonlinear differential equations, numerical simulations have contributed to great progress in fundamentally understanding the mechanism driving gas production and in developing effective exploitation methods. Owing to the substantial fundamental physics involved in the exploitation of natural gas hydrates, existing challenges, alternative strategies, and future directions are provided correspondingly from a practical application perspective.