We consider one-sided interference channel with two independent source-destination pairs, and a cognitive relay with only a link to the destination that observes interference. We first assume the relay non-causally obtains the signal messages (message cognitive) whereas the sources do not cooperate, and provide a general achievable rate region for the Gaussian case. We further analyze a more realistic set-up where instead of source messages, the relay knows the transmitted signals of both sources and is unaware of the codebooks. We investigate the achievable region under this signal cognitive assumption and further obtain a converse, thereby the capacity region under strong relay-interference conditions. Our results suggest that while relaying is usually utilized as an effective technique for boosting received signal quality, in the presence of interference, an equally important task of the relay is to manage the interference.