Language processing from the cochlea to auditory association cortices shows side-dependent specificities with an apparent left hemispheric dominance. The aim of this article was to propose to nonspeech specialists a didactic review of two complementary theories about hemispheric asymmetry in speech processing. Starting from anatomico-physiological and clinical observations of auditory asymmetry and interhemispheric connections, this review then exposes behavioral (dichotic listening paradigm) as well as functional (functional magnetic resonance imaging and positron emission tomography) experiments that assessed hemispheric specialization for speech processing. Even though speech at an early phonological level is regarded as being processed bilaterally, a left-hemispheric dominance exists for higher-level processing. This asymmetry may arise from a segregation of the speech signal, broken apart within nonprimary auditory areas in two distinct temporal integration windows—a fast one on the left and a slower one on the right—modeled through the asymmetric sampling in time theory or a spectro-temporal trade-off, with a higher temporal resolution in the left hemisphere and a higher spectral resolution in the right hemisphere, modeled through the spectral/temporal resolution trade-off theory. Both theories deal with the concept that lower-order tuning principles for acoustic signal might drive higher-order organization for speech processing. However, the precise nature, mechanisms, and origin of speech processing asymmetry are still being debated. Finally, an example of hemispheric asymmetry alteration, which has direct clinical implications, is given through the case of auditory aging that mixes peripheral disorder and modifications of central processing.