Media firms compete in two connected markets. They face rivalry for the sale of content to consumers, and at the same time, they compete for advertisers seeking access to the attention of these consumers. We explore the implications of such two-sided competition on the actions and source of profits of media firms. One main conclusion we reach is that media firms may charge higher content prices in a duopoly than in a monopoly. This happens because competition for advertisers can reduce the return per customer impression from the ad market, making each firm less willing to underprice content to increase demand. Greater competitive intensity may thus increase content profits and decrease ad profits. These findings are in sharp contrast to those in a regular one-sided product market, in which competition typically lowers product prices and profits. We extend the framework to examine competition across different media (e.g., between magazines and cable TV) and show that firms in a duopolistic medium may benefit from more intense competition from a monopolist in another medium. We characterize the conditions for each firm in the duopoly medium to bundle more ads and earn greater total profits than the rival firm in the monopoly medium.