The development of discontinuous Galerkin (DG) methods has evolved significantly since their introduction in 1973 by Reed and Hill for neutron transport. These methods have become widely used in computational fluid dynamics and various other applications due to their ability to handle discontinuities and provide high-order accuracy. DG methods are based on the finite element framework and incorporate numerical fluxes and slope limiters to capture physically relevant discontinuities without spurious oscillations. They are highly parallelizable and well-suited for complex geometries and adaptive mesh refinement. The methods have been extended to nonlinear hyperbolic systems, convection-diffusion equations, and Hamilton-Jacobi equations, leading to the development of Runge-Kutta DG (RKDG) methods for high-order accuracy and stability. Applications include gas dynamics, semiconductor device simulation, and magnetohydrodynamics. Recent developments include the local DG (LDG) method for compressible Navier-Stokes equations and the use of DG methods for Maxwell's equations. The methods have also been applied to problems involving viscoelastic flows and porous media. Overall, DG methods offer a versatile and efficient approach for solving a wide range of problems in science and engineering.The development of discontinuous Galerkin (DG) methods has evolved significantly since their introduction in 1973 by Reed and Hill for neutron transport. These methods have become widely used in computational fluid dynamics and various other applications due to their ability to handle discontinuities and provide high-order accuracy. DG methods are based on the finite element framework and incorporate numerical fluxes and slope limiters to capture physically relevant discontinuities without spurious oscillations. They are highly parallelizable and well-suited for complex geometries and adaptive mesh refinement. The methods have been extended to nonlinear hyperbolic systems, convection-diffusion equations, and Hamilton-Jacobi equations, leading to the development of Runge-Kutta DG (RKDG) methods for high-order accuracy and stability. Applications include gas dynamics, semiconductor device simulation, and magnetohydrodynamics. Recent developments include the local DG (LDG) method for compressible Navier-Stokes equations and the use of DG methods for Maxwell's equations. The methods have also been applied to problems involving viscoelastic flows and porous media. Overall, DG methods offer a versatile and efficient approach for solving a wide range of problems in science and engineering.