In this talk, I will present our recent work in developing high order central discontinuous Galerkin (DG) methods for Hamilton-Jacobi (H-J) equations and ideal MHD equations. Originally introduced for hyperbolic conservation laws, central DG methods combine ideas in central schemes and DG methods. They avoid the use of exact or approximate Riemann solvers, while evolving two copies of approximating solutions on overlapping meshes. To devise Galerkin type methods for H-J equations, the main difficulty is that these equations in general are not in the divergence form. By recognizing a weighted-residual or stabilization-based formulation of central DG methods when applied to hyperbolic conservation laws, we propose a central DG method for H-J equations. Though the stability and the error estimate are established only for linear cases, the accuracy and reliability of the method in approximating the viscosity solutions are demonstrated through general numerical examples. This work is jointly done with Sergey Yakovlev. In the second part of the talk, we introduce a family of central DG methods for ideal MHD equations which provide the exactly divergence-free magnetic field. Ideal MHD system consists of a set of nonlinear hyperbolic equations, with a divergence-free constraint on the magnetic field. Though such constraint holds for the exact solution as long as it does initially, neglecting this condition numerically may lead to nonphysical features of approximating solutions or numerical instability. This work is jointly done with Liwei Xu and Sergey Yakovlev.