  We develop first steps in the study of factorizations of elements in
ultraproducts of commutative cancellative monoids into irreducible elements. A
complete characterization of the (multi-)sets of lengths in such objects is
given. As applications, we show that several important properties from
factorization theory cannot be expressed as first-order statements in the
language of monoids, and we construct integral domains that realize every
multiset of integers larger $1$ as a multiset of lengths. Finally, we give a
new proof (based on our ultraproduct techniques) of a theorem by Geroldinger,
Schmid and Zhong from additive combinatorics and we propose a general method
for applying ultraproducts in the setting of non-unique factorizations.
