This paper draws on the simple observation that young children acquire the constraints on negative polarity items (NPIs) with relative ease and speed, and, against the backdrop of existing theoretical proposals about licensing, identifies a fundamental learning puzzle. We will begin with an overview of the methods that have been used to tap into normally-developing English-speaking children's knowledge of NPI any; such methods have revealed evidence of adult-like knowledge of the licensing condition on any in children as young as 2-3 years of age. To address the question of how children get to this stage, I examine samples of caregiver input, and discuss how they reveal different kinds of evidence for any's restricted distribution and its licensers. Importantly however, I argue that the caregiver input does not provide direct evidence of the underlying semantics of any. If only a subset of what must be acquired is present in the input, we are left with a puzzling learning problem about how children arrive at the target representation of NPIs such as any.