Abstract: In an online talk from 2022, Larry Guth considered the Mizohata-Takeuchi conjecture for the parabola and demonstrated that any improvement beyond a R^{1/3} loss needed tools beyond wavepackets and Fourier decoupling. In 2023, Tony Carbery, Marina Iliopoulou and Hong Wang attained this loss (in the case of the parabola and the paraboloid in general) as a consequence of refined decoupling. In joint work with Tony Carbery, Yixuan Pang, and Po-Lam Yung, we generalise this work to the moment curve, thus proving a version of the Mizohata-Takeuchi conjecture for "well-curved" curves with a loss that matches the numerology of Carbery-Iliopoulou-Wang for the parabola. In this talk, we will discuss the history of and progress towards the Mizohata-Takeuchi conjecture, refined decoupling, and some aspects of the proof I found quite interesting.