Automatic interpretation of Remote Sensing (RS)images and the growing interest for query by image content from large Remote Sensing Image Archives rely on the ability and robustness of information extraction from observed data. In these twoParts I and II of this article, we turn the attention to the modern Bayesian way of thinking and introduce a pragmatic approach to extract structural information from RS images by selecting from a library of a priori models those which best explain the structures within an image. Part I introduces the Bayesian approach and defines the information extraction as a two-level procedure: 1) model fitting, which is the incertitude alleviation over the model parameters, and 2) model selection, which is the incertitude alleviation over the class of models. The superiority of the Bayesian results is commented from an information theoretical perspective. The theoretical assay concludes with the proposal of a new systematic method for scene understanding from Remote Sensing images: search for the scene which best explains the observed data. The method is demonstrated for high accuracy restoration of Synthetic Aperture Radar (SAR) images with emphasis on new optimization algorithms for simultaneous model selection and parameter estimation. Examples are given for three families of Gibbs Random Fields (GRF) used as prior model libraries. Part B expands in detail on the information extraction using GRFs at one and multiple scales. Based on the Bayesian approach a new method for optimal joint scale and model selection is demonstrated. Examples are given using a nested family of GRFs utilized as prior models for information extraction with applications both to SAR and optical images.