Almost twenty years ago, Witten made a conjecture for the simple (ADE) singularities singularities, relating intersection theory on certain moduli spaces associated to each singularity and certain integrable hierarchies arising from the singularity. That conjecture was proved in the case of A_n singularities by Faber, Shadrin, and Zvonkine in 2006. Ruan, Fan, and I proved the conjecture for the D and E singularities last year. \tIn this talk I will provide a survey of Landau-Ginzburg A-models, and describe the key steps in our proof of the Witten conjecture.