Matter-wave inertial sensing relies on the capability of manipulating the coherent wave nature of matter to build an interferometer and accurately measure a phase difference. Since the massive particle associated to the matter wave senses inertial effects, the interferometer represents an accurate inertial probe. Atom interferometers have benefited from the outstanding developments of laser-cooling techniques and reached accuracies comparable to those of inertial sensors based on optical interferometry. Thanks to their long term stability, they offer a breakthrough advance in accelerometry, gyroscopy and gravimetry, for applications to inertial guidance, geoid determinations, geophysics and metrology. They are also excellent candidates for laboratory-based tests of general relativity that could compete with the current tests using astronomical or macroscopic bodies. For example, they may provide new answers to the question of whether the free fall acceleration of a particle is universal, i.e. independent of its internal composition and quantum properties. We report here the first operation of an airborne quantum inertial sensor. We highlight their promising applications to inertial navigation and Earth observation. We also describe the improvement of the quantum sensor sensitivity in weightlessness, and discuss the possibility to conduct airborne or spaceborne tests of the Universality of Free Fall with quantum objects. We finally describe a matter-wave laser based interferometric gravitational antenna (MIGA). This infrastructure will allow for measuring with unprecedented resolution variations of the Earths gravity and of the strain of space-time allowing for enhancing the capabilities of existing and future gravitational wave detectors.< Réduire