One of the major areas of research into early cognitive development concerns infants' ability to understand number, given that it leads into later numerical and mathematical competence. Accordingly, there is considerable research on this topic and there is a large body of research suggesting that infants have a least some ability to discriminate between small number sets and large number sets. This chapter begins by describing the evidence for two types of representations of number-one for small item sets, the other for large-together with evidence that these systems are modality-general. This is followed by evidence suggesting that infants may sometimes be responding to continuous variables that are found in displays of discrete items rather than number per se. It then turns to the main focus of the chapter, which is whether infants can add and subtract, or whether their purported arithmetical abilities can be explained in lower-level perceptual terms. It is in this context that the relative contributions of information-processing perspectives are compared with other theoretical views on our understanding of infants' numerical abilities.