More than a century after it was first suggested that behaviors such as speech production and perception might be lateralized in the human brain, many basic questions still remain regarding the nature and basis of right-left functional asymmetries (FAs). The lack of answers to what seem to be a straightforward set of questions may be due to two methodological aspects of laterality research which have hampered work in brain and behavior in general and lateralities in particular. The first is the absence of a biologically based, psychophysically-defined taxonomy of stimulus/gesture features for use in tests of laterality. As a result, many researchers resort to cognitive constructs for describing the bases of asymmetries, a decision which has created a gulf separating experimental as well as theoretical work on asymmetries from the biological realities of sensory and motor processing, within the brain as well as at the body periphery. The second obstacle is the lack of a valid taxonomy for individuals. Individual differences are ubiquitous in human subjects as well as non-human animals, yet are typically averaged away as noise rather than respected as possible sources of information. Studies of asymmetry often reveal dramatic individual differences in both the direction and magnitude of asymmetries, yet, when subjected to averaging and group statistics, these often result in insignificant results. This paper reviews two taxonomies which may address some of these problems: the EPIC Model of Functional Asymmetries, and the related Trimodal Model of Brain Organization. The EPIC model classifies functional asymmetries according to four domains (Extrapersonal space, Peripersonal space, Intrapersonal space, and Coordination) and assigns responsibility for these four domains differentially to the two cerebral hemispheres -- the right side is seen as "polypotent," responsible for processing in three of the domains, while the left side focuses on processing in peripersonal space. The EPIC model also proposes a "periodic chart" of complementary stimulus/gesture features which distinguish extrapersonal vs. peripersonal space, with analogues in all four somatic systems -- visual, auditory, somatosensory, and motor. The Trimodal model is based on research in psychoimmunoneuroendocrinology, and posits a continuum of individual differences created as a result of prenatal exposure to testosterone, and articulated in terms of access to the skills of the four EPIC domains. These two models together may yield guidelines not only for designing stimulus/task combinations but also for addressing individual differences.