In this talk, we discuss and analyze two novel two-level hybrid Schwarz preconditioners for solving the Helmholtz equation with high wave number in both two and three dimensions.Both preconditioners are defined over a set of overlapping subdomains, with each preconditioner formed by a global coarse solver and one local solver on each subdomain. The global coarse solver is based on the localized orthogonal decomposition (LOD) technique, which was proposed originally for the discretization schemes for elliptic multiscale problems with heterogeneous and highly oscillating coefficients and Helmholtz problems with high wave number to eliminate the pollution effect.  The local subproblems are Helmholtz problems in subdomains with homogeneous boundary conditions (for the first preconditioner) or impedance boundary conditions (for the second preconditioner). Both preconditioners are shown to be optimal under some reasonable conditions, that is, a uniform upper bound of the preconditioned operator norm and a uniform lower bound of the field of values are established in terms of all the key parameters, such as the fine mesh size, the coarse mesh size, the subdomain size and the wave numbers. This is the first time to show the rigorous optimality of a two-level Schwarz-type preconditioner with respect to all the key parameters and that the LOD solver can be a very effective coarse solver when it is used appropriately in the Schwarz method with multiple overlapping subdomains for the Helmholtz equation with high wave number. Numerical experiments are presented to confirm the optimality and efficiency of the two proposed preconditioners.