The spectrum covered by the minisymposium ranges from recent development,analysis,implementation and applications,for the weighted essential non-oscillatory(WENO)methods.The WENO methods provide a practical effective framework to solve out many nonlinear wave-dominated problems with discontinuities or sharp gradient regions,which play an important role arising in many applications of computational fluid dynamics,computational astrophysics,computational plasma physics,semiconductor device simulations,among others.Devising robust,accurate and efficient WENO methods for solving these problems is of considerable importance and,as expected,has attracted the interest of many researchers and practitioners.This minisymposium serves as a good forum for researchers to exchange ideas and to promote this active and important research direction.