Living Reviews in Computational Astrophysics is a peer-reviewed, platinum* open access journal, publishing reviews of research in all areas of computational astrophysics. Articles are solicited from leading authorities and are directed towards the scientific community at or above the graduate-student level. The articles in Living Reviews provide critical reviews of the current state of research in the fields they cover. Written by experts, reviews published in the journal cite, explain, and assess the most relevant, interesting, and important print and electronic resources in a given field. The articles evaluate existing work, place it in a meaningful context, and suggest areas where more work and new results are needed. Articles also offer annotated insights into the key literature and describe other available resources. Living Reviews is unique in maintaining a suite of high-quality reviews, which are kept up-to-date by the authors. This is the meaning of the word "living" in the journal's title.