We can retroactively edit our conscious experience.

Have you ever had the experience of tuning out someone who was droning on in a conversation or lecture that was boring you, then when suddenly being challenged by "Are you listening, what did I just say?," being surprised that you could summon up some recall of what they said, even though you had been completely ignoring it? This would be an example of how our perceptions and our consciousness can be two different things. We experience time very differently from what it really is, subjective and objective time are not the same. Our consciousness is more than just a movie that's playing in your head that you see once the processing is done. For example, recent work from Sergent and collaborators suggests that we can go back in time for at least a half a second and reintegrate something into our experience that we had previously ignored. From a review by Tia Ghose:

Study participants were shown groups of lines appearing in a circle on either the right or the left side of the screen before they disappeared. Sometimes the lines were too faint to consciously notice, while other times they were very obvious. In some of the trials where the lines were very faint, the researchers drew participants' attention to the spot where the lines had been by briefly dimming the circle — creating more contrast between the circle and the background. That "cueing of attention" happened up to a half-second after the lines disappeared. Afterward, the team asked the students what they saw. When the team had drawn attention to the spot where the lines had been, people were more likely to report having seen them "quite well." In essence, the participants had experienced retro-perception, the bizarre experience in which their brains added the lines to their conscious memory after the lines had disappeared.

Here is the Sergent et al. abstract:

Is our perceptual experience of a stimulus entirely determined during the early buildup of the sensory representation, within 100 to 150 ms following stimulation? Or can later influences, such as sensory reactivation, still determine whether we become conscious of a stimulus? Late visual reactivation can be experimentally induced by postcueing attention after visual stimulus offset [5]. In a contrary approach from previous work on postcued attention and visual short-term memory, which used multiple item displays [6 and 7], we tested the influence of postcued attention on perception, using a single visual stimulus (Gabor patch) at threshold contrast. We showed that attracting attention to the stimulus location 100 to 400 ms after presentation still drastically improved the viewers’ objective capacity to detect its presence and to discriminate its orientation, along with drastic increase in subjective visibility. This retroperception effect demonstrates that postcued attention can retrospectively trigger the conscious perception of a stimulus that would otherwise have escaped consciousness. It was known that poststimulus events could either suppress consciousness, as in masking, or alter conscious content, as in the flash-lag illusion. Our results show that conscious perception can also be triggered by an external event several hundred ms after stimulus offset, underlining unsuspected temporal flexibility in conscious perception.