Over the past few decades, considerable progress has been achieved in the theoretical predictions of a wide range of properties of defects in semiconductors In addition to structures, energetics, spin and charge densities, theory now routinely predicts accurate vibrational properties of defects, and thus connects to the optical characterization of light impurities However, the positions of gap levels have yet to be predicted with systemically reliable accuracy Today, supercells much larger than in the past are being Used to describe defect centers from first principles Systems large enough to Study the dynamics of extended defects can be handled new the first-principles level This paper contains a brief review of the key developments that have rendered theory quantitatively useful to experimentalists and an overview of the current 'state-of-the-art' and ongoing developments Some of the remaining challenges are discussed, with examples in Si and Ge Published by Elsevier B.V.