There is evidence that nonhuman animals that have not evolved a mindreading capacity, such as macaques and rodents, are nevertheless able to appropriately evaluate their self-confidence level in perceptual and memory tasks. This creates a puzzle, because self-knowledge seems to require embedding a representation into another, i.e. metarepresenting one’s own states, as exemplified in mindreading. Part of the puzzle has to do with disunified terminology. “Meta”, it is often claimed, means “being about”. “Metacognition”, then, is taken to refer to cognition about one’s own cognition, “thinking about one’s own thinking”, or, in short, to meta-knowledge. This terminology owes its influence to the early models of the relations between the control and monitoring aspects of metamemory. To philosophers, this acception of metacognition is consonant with deeply entrenched views about the exclusively human character of rationality. Caution, however, is needed to disentangle the terminological from the empirical issues: terminology should follow, rather than preempt, research. Section 1 will present the evidence. Section 2 will discuss the view that metacognition is self-directed metarepresentation. Section 3 will discuss the “no-metacognition” view, which claims that animals merely rely on observable stimuli – such as an oscillating behavior – or on anticipated reward to decide what to do. Section 4 will present the “experience-based” accounts, in which metacognition is neither a mere matter of first-order cognition, nor of metarepresentation. It will be proposed that animal metacognition depends on a non-propositional evaluative attitude called affordance-sensing, which is common to human and some nonhuman cognitive systems.