The role of inventory in explaining the shape of the forward curve and spot price volatility in commodity markets is central in the theory of storage developed by Kaldor (1939) and Working. Fama and French (1987) revisit the relationship between inventory and spot price volatility in the case of metals and use as a proxy for inventory the adjusted spread of the forward curve. The goal of our talk is threefold: i) review some interesting features of energy commodity forward curves in the recent past; ii)validate in the case of oil and natural gas the use of the slope of the forward curve as a proxy for inventory (the slope being defined in a way that filters out seasonality for natural gas); iii)) analyze directly for these two major commodities the relationship between inventory and price volatility. In agreement with the theory of storage, we find that a) the negative correlation between price volatility and inventory is globally significant for crude oil; b) this negative correlation prevails only during those periods of scarcity when the inventory is below the historical average and increases importantly during winter periods for natural gas. Our results are illustrated by the analysis of a 15 year-database of US oil and natural gas prices and inventories