She was a speaker at the 1990 International Congress of Mathematicians, on decomposition into distinguished subspaces of certain spaces of square-integral automorphic forms.
[M91][2] She was a recipient of the Jaffé prize of the French Academy of Sciences in 2004, "for her work, most notably on the topics of enveloping algebras of Lie algebras, automorphic forms and the classification of square-integrable representations of reductive classical p-adic groups by their cuspidal representations".
A prominent example of her achievements in the former is her classification, obtained with Jean-Loup Waldspurger, of the non-cuspidal discrete factors in the decomposition into irreducible components of the spaces of square-integrable invariant functions on adelic general linear groups.
[MW94] Another notable work in the domain, with Waldspurger and Marie-France Vignéras, is a book on the Howe correspondence.
[MVW] With Waldspurger, Moeglin completed the proof of the local Gan–Gross–Prasad conjecture for generic L-packets of representations of orthogonal groups in 2012.