Over the past hundred years, a number of scientific investigators claim to have adduced experimental evidence for “psi” phenomena – that is, the apparent ability to receive information shielded from the senses (ESP) and to influence systems outside the sphere of motor activity (PK). A report of one series of highly significant psi experiments and the objections of critics are discussed in some depth. It is concluded that the possibility of sensory cues, machine bias, cheating by subjects, and experimenter error or incompetence cannot reasonably account for the significant results. In addition, less detailed reviews of the experimental results in several broad areas of psi research indicate that psi results are statistically replicable and that significant patterns exist across a large body of experimental data. For example, a wide range of research seems to converge on the idea that, because ESP “information” seems to behave like a weak signal that has to compete for the information-processing resources of the organism, a reduction of ongoing sensorimotor activity may facilitate ESP detection. Such a meaningful convergence of results suggests that psi phenomena may represent a unitary, coherent process whose nature and compatibility with current physical theory have yet to be determined. The theoretical implications and potential practical applications of psi could be significant, irrespective of the small magnitude of psi effects in laboratory settings.