Capturing the breadth and variety of children's understanding is critical if studies of children's mathematical thinking are to inform policy and practice in early childhood education. This article presents an investigation of young children's counting. Detailed coding and analyses of assessment interviews with 476 preschoolers revealed understandings that would be overlooked by solely assessing the accuracy of their responses. In particular, many children demonstrated understandings of counting principles on a challenging task that were not captured by other, simpler tasks. We conclude that common approaches to capturing young children's mathematical understanding are likely underestimating their capabilities. This study contributes to researchers' understanding of what making sense of counting looks and sounds like for preschool age children (3-5 years), the development and relations among counting principles (one-to-one, cardinal, and patterns of the number sequence), and the affordances of challenging, open-ended tasks. We close by considering the implications of recognizing and building from what children know and can do for researchers, practitioners, and policymakers.