The field of satellite communications is enjoying a renewed interest in the global telecom market, and very high throughput satellites (V/HTS), with their multiple spot-beams, are key for delivering the future rate demands. In this article the state-of-the-art and open research challenges of signal processing techniques for V/HTS systems are presented for the first time, with focus on novel approaches for efficient interference mitigation. The main signal processing topics for the ground, satellite, and user segment are addressed. Also, the critical components for the integration of satellite and terrestrial networks are studied, such as cognitive satellite systems and satellite-terrestrial backhaul for caching. All the reviewed techniques are essential in empowering satellite systems to support the increasing demands of the upcoming generation of communication networks.2 SatCom system when compared to its terrestrial counterparts, including satellite channels, system constraints, and processing.Today there are approximately 1300 fully operational communication satellites. Every type of orbit has an important role to play in the overall communications system. Geostationary earth orbit (GEO), at 35,000 km, present an end-to-end propagation delay of 250 ms; therefore, they are suitable for the transmission of delay-tolerant data. Medium earth orbit (MEO), at 10,000 km, introduce a typical delay of 90 ms; based on that, they can offer a compromise in latency and provide fiber-like data rates. Finally, low earth orbit (LEO) is at between 350 and 1,200 km, and introduce short delays that range from 20 to 25 ms. In all these cases, the satellite is a very particular wireless relaying node, whose specificities lead to a communication system that cannot be treated like a wireless terrestrial one. This is because the channel, communication protocols, and complexity constraints of the satellite system create unique set of features [2], notably:• Due to the long distance to be covered from the on-ground station to the satellite, the satellite communication link may introduce both a high round-trip delay and a strong path-loss of hundreds of dB. To counteract the latter, satellites are equipped with highpower amplifiers (HPA) that may operate close to saturation and create intermodulation and nonlinear impairments.• Satellite communications traverse about 20 km of atmosphere and introduce high molecular absorption, which is even higher in the presence of rain and clouds, particularly for frequencies above 10 GHz. Therefore, satellite links are designed based on thermal noise limitations and on link budget analysis that considers large protection margins for additional losses (e.g., rain attenuation).• In the non-geostationary orbits (i.e., MEO and LEO), there are high time-channel variations due to the relative movement of the satellites with respect to the ground station.• Due to the long distance and carrier frequencies, the satellite antenna feeds are generally seen as a point in the far-field, thus making the use of spat...