This talk is mainly on recent paper joint with Jon Brundan and Peter McNamara, which develops standard module theory and "standard homological properties" for Khovanov-Lauda-Rouquier algebras of finite Lie type. Under the KLR-categorification standard modules correspond to Lusztig's PBW basis elements obtained using braid group action and parameterized by reduced decompositions of the longest element in the Weyl group. Some of these results were first obtained by S. Kato by geometric methods.