Natural gas is an important source of energy in the global economy, hence understanding the drivers of its prices is of significant interest for economic agents. This paper investigates the role of structural shocks for the dynamics of the U.S. natural gas market within the Bayesian Structural Vector Autoregression framework applied by Baumeister and Hamilton (2019a, AER), to the crude oil market. This approach provides clear intuition for the identification strategy and allows us to correctly estimate the short-term price elasticity of natural gas supply and demand. Our results indicate that the former is low, whereas the latter is higher than the average estimate in the literature. We also show that market specific demand shocks explain a dominant fraction of natural gas prices variability, while the contribution of supply, aggregate economic activity and inventory shocks is important only during specific market events such as the recent outbreak of the COVID-19 pandemic. Finally, we illustrate how changes in supply in the era of shale gas revolution contributed to the dynamics of natural gas prices.