Turbulent combustion is an extremely challenging “multi-multi” problem: multi-physics, multi-scale, and multi-species. Since not all scales of turbulence and combustion can be resolved in DNS for practical conditions of interest, models are required for the unresolved turbulent combustion processes in LES and RANS. However, the large number of thermochemical scalars required to describe combustion chemistry (potentially hundreds or thousands of chemical species) means that the unresolved state-space that needs to be modeled is extremely high-dimensional. Turbulent combustion models can generally be divided into two distinct classes based on how this dimensionality challenge is addressed. In the first class of models, no attempt is made to reduce the dimensionality of the unresolved state-space (“brute-force” models). While very general, these approaches are extremely computationally intensive and realistically impractical. Conversely, in the second class of models, the dimensionality of the unresolved state-space is reduced by a priori presuming that combustion occurs in one of the asymptotic “modes” of nonpremixed combustion, premixed combustion, or homogeneous autoignition, each of which can be described by simple one-dimensional manifold equations. While this results in a substantial reduction in computational cost, these models are not generally applicable to “multi-modal” combustion processes characteristic of practical systems. In this seminar, recent efforts to overcome this fundamental modeling trade-off will be discussed. Our new turbulent combustion modeling framework is both computationally efficient and extremely general, requiring no a priori knowledge about the underlying combustion processes in order to reduce the dimensionality of the unresolved state-space. The new approach relies on two game-changing components: (1) generalized two-dimensional manifold equations capable of describing arbitrary “multi-modal” combustion processes and (2) sensible computational algorithms that shift away from unnecessary precomputation and high-dimensional pretabulation toward ‘just-in-time’ computation and adaptive tabulation. Preliminary application with LES to canonical turbulent flames will be briefly discussed.