The ability to think about nonpresent time is a crucial aspect of human cognition. Both the past and future imply a temporal displacement of an event outside the "now." They also intrinsically differ: The past refers to inalterable events; the future to alterable events, to possible worlds. Are the past and future processed similarly or differently? In this study, we addressed this question by investigating how Spanish speakers process past/future time reference violations during sentence processing, while recording eye movements. We also investigated the role of verbs (in isolation; within sentences) and adverbs (deictic; nondeictic) during time processing. Existing accounts propose that past processing, which requires a link to discourse, is more complex than future processing, which-like the present-is locally bound. Our findings show that past and future processing differs, especially at early stages of verb processing, but this difference is not limited to the presence/absence of discourse linking. We found earlier mismatch effects for past compared to future time reference in incongruous sentences, in line with previous studies. Interestingly, it took longer to categorize the past than the future tense when verbs were presented in isolation. However, it took longer to categorize the future than the past when verbs were presented in congruous sentences, arguably because the future implies alterable worlds. Finally, temporal adverbs were found to play an important role in reinspection and reanalysis triggered by the presence of undefined time frames (nondeictic adverbs) or incongruences (mismatching verbs).