  We give a moduli-theoretic treatment of the existence and properties of
moduli spaces of semistable quiver representations, avoiding methods from
geometric invariant theory. Using the existence criteria of
Alper--Halpern-Leistner--Heinloth, we show that for many stability functions,
the stack of semistable representations admits an adequate moduli space, and
prove that this moduli space is proper over the moduli space of semisimple
representations. We construct a natural determinantal line bundle that descends
to a semiample line bundle on the moduli space and provide new effective bounds
for global generation. For an acyclic quiver, we show that this line bundle is
ample, thus giving a modern proof of the fact that the moduli space is
projective.
