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.