The article reviews the theoretical approach to the emission of gravitational waves by isolated systems in the context of general relativity. Part I focuses on general post-Newtonian sources, investigating the exterior field using a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far zone are described by radiative multipole moments, and the explicit expressions for the source multipole moments are derived by matching the exterior solution to the post-Newtonian source in the near zone. The relationships between radiative and source moments involve nonlinear multipole interactions, including those associated with gravitational wave tails. Part II applies these results to compact binary systems, presenting the equations of binary motion, the associated Lagrangian and Hamiltonian at the third post-Newtonian (3PN) order. The gravitational-wave energy flux, accounting for relativistic corrections in the binary moments and various tail effects, is derived up to 3.5PN order. The orbital phase, crucial for searching and analyzing signals from inspiralling compact binaries, is deduced from an energy balance argument. The article also discusses the finite-size effects of compact objects and the high-order post-Newtonian corrections needed for accurate predictions in LIGO and VIRGO data analysis.The article reviews the theoretical approach to the emission of gravitational waves by isolated systems in the context of general relativity. Part I focuses on general post-Newtonian sources, investigating the exterior field using a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far zone are described by radiative multipole moments, and the explicit expressions for the source multipole moments are derived by matching the exterior solution to the post-Newtonian source in the near zone. The relationships between radiative and source moments involve nonlinear multipole interactions, including those associated with gravitational wave tails. Part II applies these results to compact binary systems, presenting the equations of binary motion, the associated Lagrangian and Hamiltonian at the third post-Newtonian (3PN) order. The gravitational-wave energy flux, accounting for relativistic corrections in the binary moments and various tail effects, is derived up to 3.5PN order. The orbital phase, crucial for searching and analyzing signals from inspiralling compact binaries, is deduced from an energy balance argument. The article also discusses the finite-size effects of compact objects and the high-order post-Newtonian corrections needed for accurate predictions in LIGO and VIRGO data analysis.