Point defects in semiconductors and insulators form an exciting system for realizing quantum technologies, including quantum computing, communication, and metrology. Defects provide a platform that combines the environmental isolation necessary to maintain the coherence of quantum states with the ability to perform electrical and optical manipulation. First principles calculations play a crucial role in identifying, characterizing, and developing defects for quantum applications. We review the first-principles methodologies for calculating the relevant structural, electronic, vibrational, optical, and magnetic properties of defects for quantum technologies. We illustrate the utility and accuracy of these techniques by using examples from the literature. We also point out areas in which further development of the computational techniques is desirable. Expected final online publication date for the Annual Review of Materials Research Volume 48 is July 1, 2018. Please see http://www.annualreviews.org/page/jo...