The fact that spacecraft faces a rich and complex dynamic environment makes the development of vibration control and energy harvesting techniques a special concern in space engineering. Nonlinear Energy Sink is such a technique that has developed recently. It generally refers to a lightweight nonlinear device, that is attached to a primary system with essential nonlinear couplings. A special one-way energy transfer called targeted energy transfer (TET) could be observed for passive energy localization into itself. By taking advantage of such essential nonlinearities and the TET phenomenon, NES could be designed as smart and lightweight vibration absorbers or energy harvesters, in a broadband manner, which is especially suitable for the need in aerospace engineering. This chapter is thus devoted to the nonlinear dynamics of vibrational systems with coupled NESs and their applications in the field of passive vibration suppression and vibration energy harvesting.