Our understanding of stars is built on models of how heat, momentum, and chemical elements are transported in their interiors. In recent years, asteroseismology, broad spectroscopic surveys and spectropolarimetric measurements have dramatically improved our ability to probe these transport phenomena. These new data, as well as improved numerical simulations, show that key uncertainties in stellar models lie in treatments of turbulence, magnetism, and wave phenomena. This program will bring together experts in stellar observations, 1D stellar evolution, and 3D stellar modeling, to (1) Summarize and sharpen discrepancies between stellar theory and observations; (2) Enable and encourage incorporation of results from 3D simulations in 1D stellar evolution, while also testing 1D transport theories in 3D simulations; (3) Identify new methods to probe stellar interiors, either via new instruments and telescopes or new theoretical and data-analytic approaches.