(The talk is aimed at early graduate students)
Decoupling estimates were introduced by Wolff  in order to improve local smoothing estimates for the wave equation. Since then, they have found multiple applications in analysis: from PDEs and restriction theory, to additive number theory, where Bourgain, Demeter and Guth used decoupling-type estimates to prove the main conjecture of the Vinogradov mean value theorem for d>3.
In this talk I will explain what decoupling estimates are, I will talk about its applications to the Vinogradov Mean Value theorem and local smoothing, and I will explain the main ingredients that go into (most) decoupling proofs
 Wolff, T. (2000). Local smoothing type estimates on Lp for large p. Geometric & Functional Analysis GAFA
 Bourgain, J., Demeter, C., & Guth, L. (2016). Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three. Annals of Mathematics, 633-682.