  Courant algebroids provide a useful mathematical tool (not only) in string
theory. It is thus important to define and examine their morphisms. To some
extent, this was done before using an analogue of canonical relations known
from symplectic geometry. However, it turns out that applications in physics
require a more general notion. We aim to provide a self-contained and detailed
treatment of Courant algebroid relations and morphisms. A particular emphasis
is placed on providing enough motivating examples. In particular, we show how
Poisson-Lie T-duality and Kaluza-Klein reduction of supergravity can be
interpreted as Courant algebroid relations compatible with generalized metrics
(generalized isometries).
