We define forward entrainment as that part of behavioral or neural entrainment that outlasts the entraining stimulus. In this review, we examine conditions under which one may optimally 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, and 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 describe those experimental conditions that place constraints on the magnitude of forward entrainment, including an evaluation of the effects of signal uncertainty and attention, temporal envelope complexity, signal-to-noise ratio (SNR), rhythmic rate, prior experience, and intersubject variability. In Part 3 we theorize on potential mechanisms and propose that forward entrainment may instantiate a dynamic auditory afterimage that lasts a fraction of a second to minimize prediction error in signal processing.