This paper addresses the design of optimal and near-optimal detectors in an interference channel with fading and with additive white Gaussian noise (AWGN), where the transmitters employ discrete modulation schemes as in practical communication scenarios. The conventional detectors typically either ignore the interference or successively detect and then cancel the interference, assuming that the desired signal and/or the interference are Gaussian. This paper quantifies the significant performance gain that can be obtained if the detectors explicitly take into account the modulation formats of the desired and the interference signals. This paper first describes the optimal maximum-likelihood (ML) detector that minimizes the probability of detection error for a given modulation scheme, and the joint minimum-distance (MD) detector, which is a lower-complexity approximation of the ML detector. It is then demonstrated by analysis and by simulation that in an AWGN channel, while interference-ignorant and successive interference cancellation detectors are both prone to error floors, the optimal ML and joint MD detectors are not. This paper further analyzes the performance of joint detection in a Rayleigh fading environment. It is demonstrated that the joint detector can achieve symbol error rates that have the same dependence on the received signal-to-noise ratio (SNR) as if the channel were interference free. Thus, the performance of joint detection is fundamentally limited by the SNR rather than the signal-to-interference ratio (SIR). Moreover, the joint detector enables the use of transmit diversity schemes to achieve the same diversity order as in the absence of interference. These results show that the use of interference-aware detectors can significantly alleviate the effect of interference thereby improving the achievable rates and the reliability of future wireless systems.