A point in case is the Lieb-Oxford bound. Becke argued that any reasonable exchange functional globally satisfies the Lieb-Oxford bound for any real chemical or physical system, irrespective of whether the underlying energy density obeys or violates it locally. In other words, a local Lieb-Oxford bound seems to be a sufficient but not a necessary constraint in the design of functionals -the exact-exchange energy density, in particular, violates the local Lieb-Oxford bound in the tail of any finite system. A local enforcement of the Lieb-Oxford bound gives enhancement factors of some widely used semilocal exchange func-(e.g., PBE 234 and SCAN 235 functionals) that are somewhat too low to describe finite systems adequately (in combination with an appropriate correlation functional), thus hampering thermochemical accuracy. In recent years, a consensus seems to have developed that the most promising avenue is to find a fixed-point proof, via the force-balance equation. The latter is an equation of motion for the density, involving its second time derivative ρ(r,t), external forces, and internal kinetic and many-body stresses. The fixedpoint technique is mathematically very difficult and the TDDFT proofs based on it are still not fully rigorous. It has recently been shown that TDDFT can be reformulated using ρ(r,t) instead of ρ(r,t) as the basic variable, which has the advantage that the causal structure of the theory becomes more transparent. This result may provide a new way forward in the ongoing attempts to solidify the foundations of TDDFT. However, SCF convergence remains problematic in some cases -for instance, for large, heterogeneous, systems such as metal-insulator interfaces. Progress has been made recently, 710 based on a better understanding of the mathematical properties of the Kohn-Sham model. Some particularly difficult systems are still resisting, motivating further work in this direction.