An achievable region, outer bounds and a capacity result are established for two-sender two-receiver interference channels with one cognitive transmitter. Specifically, we assume that one transmitter knows either the full or, more realistically, the partial message of the other transmitter due to its cognitive capabilities. The achievable region is obtained by a rate-splitting strategy, which generalizes prior strategies under both weak and strong interference conditions. The outer bounds are based on an extension of the Nair-El Gamal outer bound for the broadcast channel capacity. When only the partial message is known to the cognitive user, the capacity region in strong interference is established. In this regime, the interference is such that both receivers can decode both messages with no rate penalty.