Based on both experimental and crosslinguistic evidence, this paper argues for a novel empirical generalization: infinitives crosslinguistically and within the same language are deficient in tense; in other words, they cannot bear past or present tense. First, I provide novel experimental evidence showing that infinitival tense cannot be interpreted de re. Second, I present a survey of infinitival adjunct constructions in English, Catalan, Spanish, Japanese and Korean, all of which are tenseless in different ways despite their different properties. Based on these pieces of evidence, I argue that infinitives can be tenseless in one of three ways. They can have a dependent tense specification, of which there are two types: anaphoric, de se tense for propositional and future-irrealis infinitives, or tense sharing between the matrix and embedded predicate for aspectual and eventive infinitives. The third kind of tenselessness is true tenselessness, where the temporal interpretation is merely an implicature. Finally, to help support this generalization, I provide an analysis of infinitives with the aspectual marker have in terms of anaphoric tense.