Many commodities are distributed through networks that involve a variety of means of transportation or transmission. For some, such as the electricity networks, the physical mechanism may be well understood, but the actually transmission elements may be hidden from view due to security concerns. For others, such as gasoline networks, the distribution network may involve multiple modes, such as pipeline, ship, rail, and truck, with unknown overall capacities. Observations of prices, production, and consumption may however enable discovery of the hidden structure of the network connections, their costs and capacities. This talk will describe how inverse optimization can be used to make these discoveries and will demonstrate the effectiveness of these methods using data from electricity and gasoline networks.