The usefulness of lattice codes is investigated for two-user Gaussian interference channels (IC). A coding scheme based on the compute-and-forward technique is shown to achieve the capacity region of the Gaussian IC under strong interference. The proposed scheme uses single-user decoders whereas the conventional scheme uses multi-user decoders for simultaneous decoding. The same scheme is applicable to the Gaussian Z-interference channel. A lattice-based coding scheme is also devised for the state-dependent Gaussian IC with the state sequence non-causally known to transmitters. The proposed scheme establishes new achievable rate regions, which can be considerably larger than the best known results, especially when the interfering state sequence has very large power. © 2015 IEEE.