  We define a notion of height for rational points with respect to a vector
bundle on a proper algebraic stack with finite diagonal over a global field,
which generalizes the usual notion for rational points on projective varieties.
We explain how to compute this height for various stacks of interest (for
instance: classifying stacks of finite groups, symmetric products of varieties,
moduli stacks of abelian varieties, weighted projective spaces). In many cases
our uniform definition reproduces ways already in use for measuring the
complexity of rational points, while in others it is something new. Finally, we
formulate a conjecture about the number of rational points of bounded height
(in our sense) on a stack X, which specializes to the Baytev-Manin conjecture
when X is a scheme and to Malle's conjecture when X is the classifying stack of
a finite group.
