This book was written by 76 authors, among best specialists of the field, at the intention of academics, researchers, engineers, graduated and undergraduated students wishing to update their knowledge and understanding of the covered class of materials. It contains 26 chapters on different subjects (original research articles, review articles on fundamental aspects and applications). It presents new trends and perspectives on perovskites but also on other Framework Structure crystalline materials. Perovskites are among the most famous materials due to their exceptional properties: they present nearly all existing types of interesting properties, in particular as ferroics or multiferroics, they may be insulators, (super)conductors, or semiconductors, magnetoresistant, they are used in numerous devices, they present hundreds of variants and different crystalline phases and phase transitions, and recently appeared as probably the most promising materials for photovoltaics. With a crystal structure characterized by octahedra that share their corners, these materials belong to the wider category of Framework Structure (FWS) materials the structure of which is based on units (octahedra, tetrahedra, ...) that share some of their corners (or edges) with their neighbours. This particular feature of FWS materials confers to them unique properties. This review volume is constituted of 26 chapters on different aspects, and is divided in two parts, Fundamental aspects and general properties , and Elaborated materials and applied properties . Its main purpose is to attempt to identify the properties common to all members of the vast family of FWS materials, and understand their differences. Besides perovskites, derived compounds as 2D perovskites, Dion-Jacobson, Ruddlesden-Popper, Aurivillius, tungsten-bronzes, and others, are presented, and their preparation and/or properties as single crystals, ceramics, thin films, multilayers, nanomaterials, nanofibers, nanorods, etc, are discussed. We focus on new trends and important recent developments by leaving somewhat aside more classical aspects which can be easily found in older textbooks or review articles. In conclusion, this book presents a collection of texts elucidating various aspects of the relation between structural organization (including dynamical aspects) and singular properties of framework crystals.