Physical properties and models of electronic structure are analyzed for a new class of high-TC superconductors which belong to iron-based layered compounds. Despite their variable chemical composition and differences in the crystal structure, these compounds possess similar physical characteristics, due to electron carriers in the FeAs layers and the interaction of these carriers with fluctuations of the magnetic order. A tremendous interest towards these materials is explained by the prospects of their practical use. In this monograph, a full picture of the formation of physical properties of these materials, in the context of existing theory models and electron structure studies, is given. The book is aimed at a broad circle of readers: physicists who study electronic properties of the FeAs compounds, chemists who synthesize them and specialists in the field of electronic structure calculations in solids. It is helpful not only to researchers active in the fields of superconductivity and magnetism, but also for graduate and postgraduate students and all those who would like to get acquaintained with this vivid area of the materials science.