Building upon the fundamental partial compositeness framework, we provide consistent and potentially complete composite extensions of the Standard Model. These are used to determine the effective operators emerging at the electroweak scale in terms of the standard model fields upon consistently integrating out the heavy composite dynamics. We exhibit the first effective field theories matching these composite theories of flavor and analyze their physical consequences for the third generation quarks. Relations with other approaches, ranging from effective analyses for partial compositeness to extra dimensions as well as purely fermionic extensions, are briefly discussed. Our methodology is applicable to any composite theory of dynamical electroweak symmetry breaking featuring a complete theory of flavor.