Human-centered computing (HCC) as a field was defined several years ago. Since then, the Web has grown significantly, and so has its impact in society at every level, creating the grounds for a new Web science. In this paper, we examine the definitions of HCC and Web science, and discuss how they might be related. On the one hand, HCC can be viewed as a set of methodologies, and on the other hand, Web science can be viewed as a platform or repository, from which behavioral data can be drawn. We examine the relationship between the two, and summarize three different research approaches that in many ways show this intersection.