  This article consists of an introduction to Iyama's higher Auslander-Reiten
theory for Artin algebras from the viewpoint of higher homological algebra. We
provide alternative proofs of the basic results in higher Auslander-Reiten
theory, including the existence of $d$-almost-split sequences in
$d$-cluster-tilting subcategories, following the approach to classical
Auslander-Reiten theory due to Auslander, Reiten, and Smal{\o}. We show that
Krause's proof of Auslander's defect formula can be adapted to give a new proof
of the defect formula for $d$-exact sequences. We use the defect formula to
establish the existence of morphisms determined by objects in
$d$-cluster-tilting subcategories.
