Current theories about visual perception assume that our perceptual system weights the a priori incomplete, noisy and ambiguous sensory information with previous, memorized perceptual experiences in order to construct stable and reliable percepts. These theories are supported by numerous experimental findings. Theories about precognition have an opposite point of view. They assume that information from the future can have influence on perception, thoughts, and behavior. Several experimental studies provide evidence for precognition effects, other studies found no such effects. One problem may be that the vast majority of precognition paradigms did not systematically control for potential effects from the perceptual history. In the present study, we presented ambiguous Necker cube stimuli and disambiguated cube variants and systematically tested in two separate experiments whether perception of a currently observed ambiguous Necker cube stimulus can be influenced by a disambiguated cube variant, presented in the immediate perceptual past (perceptual history effects) and/or in the immediate perceptual future (precognition effects). We found perceptual history effects, which partly depended on the length of the perceptual history trace but were independent of the perceptual future. Results from some individual participants suggest on the first glance a precognition pattern, but results from our second experiment make a perceptual history explanation more probable. On the group level, no precognition effects were statistically indicated. The perceptual history effects found in the present study are in confirmation with related studies from the literature. The precognition analysis revealed some interesting individual patterns, which however did not allow for general conclusions. Overall, the present study demonstrates that any future experiment about sensory or extrasensory perception urgently needs to control for potential perceptual history effects and that temporal aspects of stimulus presentation are of high relevance.