We define forward entrainment as that part of the entrainment process that outlasts the entraining stimulus. In this study, we examine conditions under which one may or may not observe forward entrainment. In part 1, we review and evaluate studies that have observed forward entrainment using a variety of psychophysical methods (detection, discrimination and reaction times), different target stimuli (tones, noise, gaps), different entraining sequences (sinusoidal, rectangular or sawtooth waveforms), a variety of physiological measures (MEG, EEG, ECoG, CSD), in different modalities (auditory and visual), across modalities (audiovisual and auditory- motor), and in different species. In part 2, we review those studies that have failed to observe forward entrainment, with emphasis on evaluating the methodological and stimulus design differences that may clarify the contrasting findings across these two classes of studies. In part 3, we describe those experimental conditions under which we ourselves have failed to observe forward entrainment, and provide new data on use of complex envelope patterns as entraining stimuli, show data on intersubject variability, and provide new findings on psychometric functions that characterize the strength of forward entrainment at different SNRs. In part 4 we theorize on potential mechanisms, describe how neurophysiological and psychophysical studies approach the study of entrainment, and caution against drawing direct causal inferences between the two without compelling evidence beyond correlative measures.