The Szemerédi–Trotter theorem, about the number of $r$-rich lines with respect to a given set of points, can be used to give solutions to a number of problems in discrete geometry, such as Beck's theorem and certain exceptional set estimates. Said problems in discrete geometry have analogous continuum theorems/conjectures. This includes, for instance, Orponen-Shmerkin-Wang's (2022) and Ren's (2023) continuum Beck's theorem, Ren and Wang's (2023) sharp Furstenberg set and exceptional set estimates in the plane, and B.-Marshall's (to appear) continuum Erd\H{o}s-Beck theorem. In this talk, we will begin by discussing how Szemerédi–Trotter can imply said discrete results. Then, we will highlight the connection between the discrete results and these continuum problems, as well as the tools that go into the continuum proofs (such as the use of Hausdorff dimensional results in projection theory). Lastly, we will begin to go into how these projection theory results may be obtained via delta discretization (including joint work with Shengwen Gan).