Alpha oscillations are a prominent electrophysiological signal measured across a wide range of species and cortical and subcortical sites. Alpha oscillations have been viewed for a long time as an "idling" rhythm, purely reflecting inactive sites. Despite earlier evidence from neurophysiology, awareness that alpha oscillations can substantially influence perception and behavior has grown only recently in cognitive neuroscience. Evidence for an active role of alpha for perception comes mainly from several visual, near-threshold experiments. In the current review, we extend this view by summarizing studies showing how alpha-defined brain states relate to illusory perception, i.e. cases of perceptual reports that are not "objectively" verifiable by distinct stimuli or stimulus features. These studies demonstrate that ongoing or prestimulus alpha oscillations substantially influence the perception of auditory, visual or multisensory illusions.