A challenge for statistical theory is to provide concepts unifying ideas of study design and data analysis and interpretation as they arise across the wide range of fields in which statistical ideas play some role. To what extent is this challenge met? This broad question will be illustrated with examples from the physical and social sciences and from medical statistics and epidemiology. Long standing issues about the nature of probability and of the relation between frequentist and Bayesian approaches to the formal theory of statistical inference will be touched on.