The accuracy of speech recognition systems degrades when operated in adverse acoustical environments. This paper reviews various methods by which more detailed mathematical descriptions of the effects of environmental degradation can improve speech recognition accuracy using both "data-driven" and "model-based" compensation strategies. Data-driven methods learn environmental characteristics through direct comparisons of speech recorded in the noisy environment with the same speech recorded under optimal conditions. Model-based methods use a mathematical model of the environment and attempt to use samples of the degraded speech to estimate model parameters. These general approaches to environmental compensation are discussed in terms of recent research in environmental robustness at CMU, and in terms of similar efforts at other sites. These compensation algorithms are evaluated in a series of experiments measuring recognition accuracy for speech from the ARPA Wall Street Journal database that is corrupted by artificially-added noise at various signal-to-noise ratios (SNRs), and in more natural speech recognition tasks.