In this talk, we present some recent work on discontinuous Galerkin (DG) methods for waves and fluid flow. Three topics will be covered, including (1) new energy-conserving DG methods for linear hyperbolic waves, and nonlinear dispersive waves, (2) globally divergence-free DG methods for incompressible flow, and (3) hybridizable DG methods for Darcy flow on polygonal meshes. The key idea of each DG scheme will be addressed.