Shu’s review paper on WENO

Conclusion (Active research areas):

Proper implementation of WENO in implicit solvers. Difficulties arise from the very expensive solve at each iteration of the nonlinear step. Also, large time steps have problem near strong shocks
Custom made nonlinear weights to improve WENO performance at some cases, including better accuracy at smooth regions and improved steady state convergence
Better implementations of WENO on unstructured meshes, including more investigation of robust 3D implementations
Mixing several variants of WENO schemes in one implementation to combine their advantages.
Using WENO as a limiter for Discrete Galerkin method
Custom made WENO with special properties to have better results at specific applications
Using building blocks other than polynomial for WENO interpolation might be beneficial in some cases. some ENO schemes and DG schemes already have other building blocks
Have better theoretical analysis of WENO, but not on the cost of more computation complexity or less accuracy.
Increase the class of the problems, which uses WENO