L_\infty algebras, i.e. Lie algebras up to homotopy coherent homotopy, appear in a variety of contexts, including string theory and deformation theory. Over the last several decades, the outlines of a Lie theory for such objects has appeared in work of Sullivan, Getzler, Henriques and others. In this talk, we'll present joint work with Chris Rogers (UNR) establishing Lie's second and third theorems for connective L_\infty-algebras, with a focus on Lie's third theorem as an interplay of homotopical algebra, differential topology and Lie theory.