Abstract: Iron (nickel)-based superconductors have attracted tremendous interest recently in the field of condensed matter physics, and large number of impressive works have been done both experimentally and theoretically. In particular, first-principles calculations have played an important role in the understanding of the physics. In this paper we review some basic aspects of this new class of high critical temperature superconductors, including the basic electronic structure, ground state and magnetic instability, phonon spectrum, and electron-phonon coupling, as well as the role of correlations in these compounds. We also discuss some of the diffculties encountered in first principles calculations and their possible solutions.