This paper is the first attempt to provide a comprehensive account of pricing and informational efficiency of the US and EU natural gas markets. We rely on Maximum Overlap Discrete Wavelet decomposition (MODWT) of daily data of US Henry Hub, British NBP and Dutch TTF natural gas physical and futures returns at different maturities between 2013 and 2019. Multiscale linear and nonlinear Granger causality and random walk testing are investigated. We find that futures prices and spot prices of Henry Hub, NBP, and TTF are cointegrated. Moreover, multiscale causality testing shows that Henry Hub markets exhibit strong bidirectional causality between spot and futures markets. EU markets are globally efficient in terms of pricing despite some inconsistencies on the causality direction across time scales and maturities of the futures contracts. Finally, for the three selected futures markets, informational efficiency is reached only in the long-run. The results make it possible to establish an evaluation of the hubs in terms of their capacity to provide reliable reference prices for the quantities of gas under contract through a discussion on the crucial role of liquidity and storage capacity.