A quantitative description is presented of the dynamical process of polymer intercalation into clay tactoids and the ensuing aggregation of polymer‐entangled tactoids into larger structures, obtaining various characteristics of these nanocomposites, including clay‐layer spacings, out‐of‐plane clay‐sheet bending energies, X‐ray diffractograms, and materials properties. This model of clay–polymer interactions is based on a three‐level approach, which uses quantum mechanical and atomistic descriptions to derive a coarse‐grained yet chemically specific representation that can resolve processes on hitherto inaccessible length and time scales. The approach is applied to study collections of clay mineral tactoids interacting with two synthetic polymers, poly(ethylene glycol) and poly(vinyl alcohol). The controlled behavior of layered materials in a polymer matrix is centrally important for many engineering and manufacturing applications. This approach opens up a route to computing the properties of complex soft materials based on knowledge of their chemical composition, molecular structure, and processing conditions.