Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of new and more relevant goals for probability education in the 21st century. We interviewed seven practitioners, whose professional lives are centered on probability modeling over a diverse range of fields including the development of probability theory. A thematic analysis approach produced four frameworks: (1) probability modeling approaches; (2) probabilistic thinking approaches to a problem; (3) a probability modeling cycle; and (4) core building blocks for probabilistic thinking and modeling. The main finding was that seeing structure and applying structure were important aspects of probability modeling. The implications of our findings for probability education are discussed.