Individuals of many animal species communicate with each other using sounds or "calls" that are made up of basic acoustic patterns and their combinations. We are interested in questions about the processing of communication calls and their representation within the mammalian auditory cortex. Our studies compare in particular two species for which a large body of data has accumulated: the mustached bat and the rhesus monkey. We conclude that the brains of both species share a number of functional and organizational principles, which differ only in the extent to which and how they are implemented. For instance, neurons in both species use "combination-sensitivity" (nonlinear spectral and temporal integration of stimulus components) as a basic mechanism to enable exquisite sensitivity to and selectivity for particular call types. Whereas combination-sensitivity is already found abundantly at the primary auditory cortical and also at subcortical levels in bats, it becomes prevalent only at the level of the lateral belt in the secondary auditory cortex of monkeys. A parallel-hierarchical framework for processing complex sounds up to the level of the auditory cortex in bats and an organization into parallel-hierarchical, cortico-cortical auditory processing streams in monkeys is another common principle. Response specialization of neurons seems to be more pronounced in bats than in monkeys, whereas a functional specialization into "what" and "where" streams in the cerebral cortex is more pronounced in monkeys than in bats. These differences, in part, are due to the increased number and larger size of auditory areas in the parietal and frontal cortex in primates. Accordingly, the computational prowess of neural networks and the functional hierarchy resulting in specializations is established early and accelerated across brain regions in bats. The principles proposed here for the neural "management" of species-specific calls in bats and primates can be tested by studying the details of call processing in additional species. Also, computational modeling in conjunction with coordinated studies in bats and monkeys can help to clarify the fundamental question of perceptual invariance (or "constancy") in call recognition, which has obvious relevance for understanding speech perception and its disorders in humans.