The possibility that information can be acquired at a distance without the use of the ordinary senses, that is by “extrasensory perception” (ESP), is not easily accommodated by conventional neuroscientific assumptions or by traditional theories underlying our understanding of perception and cognition. The lack of theoretical support has marginalized the study of ESP, but experiments investigating these phenomena have been conducted since the mid-19th century, and the empirical database has been slowly accumulating. Today, using modern experimental methods and meta-analytical techniques, a persuasive case can be made that, neuroscience assumptions notwithstanding, ESP does exist. We justify this conclusion through discussion of one class of homogeneous experiments reported in 108 publications and conducted from 1974 through 2008 by laboratories around the world. Subsets of these data have been subjected to six meta-analyses, and each shows significantly positive effects. The overall results now provide unambiguous evidence for an independently repeatable ESP effect. This indicates that traditional cognitive and neuroscience models, which are largely based on classical physical concepts, are incomplete. We speculate that more comprehensive models will require new principles based on a more comprehensive physics. The current candidate is quantum mechanics.