  Gaussian Processes (GPs) has experienced tremendous success in geoscience in
general and for bio-geophysical parameter retrieval in the last years. GPs
constitute a solid Bayesian framework to formulate many function approximation
problems consistently. This paper reviews the main theoretical GP developments
in the field. We review new algorithms that respect the signal and noise
characteristics, that provide feature rankings automatically, and that allow
applicability of associated uncertainty intervals to transport GP models in
space and time. All these developments are illustrated in the field of
geoscience and remote sensing at a local and global scales through a set of
illustrative examples.
