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Description: Perceptual systems have to make sense out of a world that is not only noisy and ambiguous, but that also varies from situation to situation. Human speech perception is a perceptual domain where this problem has long been acknowledged: individual talkers vary substantially in how they produce linguistic units using acoustic cues. Yet, how the speech system solves this problem of talker variability remains poorly understood. This thesis presents a computational framework---the ideal adapter---for understanding this problem and how the speech perception system solves it. The basic insight of this framework is that variability in speech is not arbitrary but rather structured: talkers are reasonably consistent in the way they produce cues, and individual talkers tend to cluster into groups by gender, regional background, etc. This structure means that listeners can use their previous experience with other talkers to guide perception of unfamiliar talkers, as well as familiar talkers that they encounter again. This framework unifies a large and messy literature on how listeners cope with talker variability, leads to quantitative models that provide good fits to human behavior in a variety of situations, and makes specific, testable predictions that open up new frontiers in understanding speech perception. This framework also applies to perception in general, and highlights how speech perception can serve as a model organism for understanding how perceptual systems cope with a variable but structured world.