This article analyses the impact of Exchange-Traded Funds (ETFs) on commodity markets. We first develop an equilibrium model where three markets are linked to each other: the spot market, where the physical trading of the commodity takes place, and the associated futures and ETF markets. Arbitrage operations link spot, futures and ETF prices together. Thanks to the model, we can study the impact of the ETF, on the long run, on the variance of commodity spot and futures prices in different situations: i) when futures prices are in contango (stocks are abundant and arbitrage is easy) and when they are in backwardation (stocks are rare and arbitrage is difficult); ii) when the ETF relies on operations on the commodity itself (physical replication) and when it relies on futures transactions (synthetic replication). The model allows to define a Vector Error Correcting representation and to obtain a price discovery metrics in the case of three markets. On the basis of this measure, we perform empirical tests on 130 ETFs on precious metals, from 2004 to 2019. We show that, in our sample, the price discovery process is shared between the spot and the ETF markets, and that the latter is most of the time dominant in terms of information flows. Finally, we propose a method that allows for the identification of the days when ETFs are active on the futures and on the spot markets of the commodity. Controlling for other possible shocks we show, on a large sample of commodity ETFs, that when the ETFs are active, the price volatility of the commodity increases, with the exception of platinum. These results have implications for commodity production, storage and transformation decision making as well as for the regulation of commodity markets.