Abstract: Extracting predictions from quantum field theories requires taming the factorial growth of perturbation theory. The modern S-matrix program has discovered a variety of tools to overcome this computational barrier, one of which being the duality between color and kinematics. The hidden graphical simplicity elucidated by color-kinematics duality could prove invaluable in computing the next generation of physical predictions across a variety of physical domains. In this talk, I will detail novel structures that have emerged at the intersection color-kinematics duality and effective field theory — from universal U(1) duality invariant building blocks, to the emergence of massive modes in color-dual gauge theories. These structures have cultivated insights into the graphical organization that underlies a vast landscape of effective field theories. I conclude by describing future applications of these insights to gravitational wave physics and inflationary observables.