I will discuss two applications of break divisors (defined in the second lecture) to the theory of algebraic curves. The first is a result of Amini describing the limiting distribution of higher Weierstrass points on an algebraic curve over a non-Archimedean field K. The limiting distribution, called the Zhang measure, has interesting interpretations in terms of break divisors, random walks, and electrical networks, and is analogous to the Bergman measure on a Riemann surface. I will also discuss the discretization of the Zhang measure, which is related to the geometric bijections from Lecture 2. The second application I will discuss is the recent work of Tif Shen, from his Yale Ph.D. thesis, relating break divisors to Simpson compactifications of Neron models.