We provide a review of results on two-sided ideals in the enveloping algebra of a locally simple Lie algebra . We pay special attention to the case when is one of the finitary Lie algebras . The main results include a description of all integrable ideals in , as well as a criterion for the annihilator of an arbitrary (not necessarily integrable) simple highest weight module to be nonzero. This criterion is new for . All annihilators of simple highest weight modules are integrable ideals for . Finally, we prove that the lattices of ideals in and are isomorphic.