Next-generation instruments to be carried onboard spacecraft are collecting a large quantity of information at an increasing rate due to recent technological improvements. The result is the increasing importance that onboard payload data compression and processing are gaining in the framework of a spacecraft design. Powerful compression algorithms are required to match the available channel resources. Moreover, many Earth Observation satellites are required to transmit data on-ground in real time, this means that compression devices with very high throughput are requested. In science missions, one of the challenges is to have the capability to transmit to ground stations a high amount of data through a limited downlink. Thanks to onboard data compression, it is possible to transmit all of the data generated onboard, without any restriction, maximizing the scientific return. Moreover, other types of processing can be done onboard, e.g. encryption, compressive sensing, and data analysis, which open the door to new applications, such as vision-based spacecraft control.