Natural gas-fired generation units help mitigate the volatility of renewable energy sources. The fast-ramping capability of gas-fired units has rendered them as one of the best solutions to possible fluctuations in the system. This chapter focuses on the modeling of natural gas system dynamics and discusses that accurate modeling is essential to manage the volatile demand of these units, particularly during short-term fluctuations. While steady-state models are commonly used to simplify these dynamics, they are argued to be unreliable for short-term operations. The chapter first discusses different approaches to modeling natural gas dynamics and present several convex relaxation methods. It also introduces techniques for the coordinated operation of interconnected electricity-gas systems. Through the case studies, the chapter presents the steady-state model of natural gas optimization and highlights its drawbacks. Finally, the chapter shows that the rank-minimization relaxation technique can accurately and efficiently solve the non-convex natural gas flow equations.