Hypnotizability is a dispositional trait reflecting the individual ability to modify perception, memory and behavior according to imaginative suggestions. It is measured by validated scales that classify the general population in high (highs), medium (mediums) and low (lows) hypnotizable persons, predicts the individual proneness to respond to suggestions, and is particularly popular in the field of the cognitive control of pain and anxiety. Different hypnotizability levels, however, have been associated with specific brain morpho-functional characteristics and with peculiarities in the cognitive, sensorimotor and cardiovascular domains also in the ordinary state of consciousness and in the absence of specific suggestions. The present scoping review was undertaken to summarize the asymmetries observed in the phenomenology and physiological correlates of hypnosis and hypnotizability as possible indices of related hemispheric prevalence. It presents the findings of 137 papers published between 1974 and 2019. In summary, in the ordinary state of consciousness, behavioral, neurophysiological and neuroimaging investigations have revealed hypnotizability related asymmetries mainly consisting of pre-eminent left hemisphere information processing/activation in highs, and no asymmetries or opposite directions of them in lows. The described asymmetries are discussed in relation to the current theories of hypnotizability and hypnosis.