Compositionality is a means of constructing complex objects through the transformation and combination of simpler elements. While it is common to view compositionality as inherently complex, and thus to assume that compositionality is a byproduct of advanced language expertise, we argue otherwise. We propose that, although compositionality produces complex outcomes, the underlying processes are simple and can often be reduced to the general mechanism of function application. Accordingly, we explore the origins of compositionality not only in compositional language but also, and at an earlier stage, in the development of compositional representations and thoughts in young infants. Infants correctly composed simple noun-verb sentences at 14 months, facial expressions with objects at 12 months, and mental physical transformations at 10 months. This offers evidence for function application, the essence of compositionality, in infancy-emerging well before and outside the development of compositional language.