We will start by introducing an important class of problems in Fourier analysis known as Fourier restriction type problems. As a modern way to attack them, one can decompose the underlying functions and then use rectangular boxes in Euclidean spaces to approximate each summand. Understanding how those boxes overlap (called an incidence problem) thus naturally play an important role in the original Fourier analytic problems. We will talk about the solutions to two such long-standing problems (Carleson's problem in high dimensions and local smoothing in three dimensions) and highlight the places where incidence estimates show up. Based on joint work with Xiumin Du and joint work with Larry Guth and Hong Wang.