This paper compares several different approaches to robust speech recognition. We review CMU's ongoing research in the use of acoustical pre-processing to achieve robust speech recognition, including the first evaluation of pre-processing in the context of the DARPA standard AXIS domain for spoken language systems. We also describe and compare the effectiveness of three complementary methods of signal processing for robust speech recognition: acoustical pre-processing, microphone array processing, and the use of physiologically-motivated models of peripheral signal processing. Recognition error rates are presented using these three approaches in isolation and in combination with each other for the speaker-independent continuous alphanumeric census speech recognition task.