The coherence time of a wireless channel is often smaller than the delay with which channel state information is available at transmitters. In this paper, we aim to find the most important subset of the channel state information that transmitters need to learn with delay. We characterize the capacity region of the two-user interference channel with local delayed channel state information at transmitters. We propose a transmission strategy that only relies on the delayed knowledge of the outgoing links at each transmitter and achieves the outer-bound for the scenario in which transmitters learn the entire channel state with delay. We also show that the delayed knowledge of the outgoing links is the minimum delayed knowledge that is required to outperform the no knowledge assumption.