The 2018 Fields Medal has been awarded to: Caucher Birkar For the proof of the boundedness of Fano varieties and for contributions to the minimal model program. Alessio Figalli For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability. Peter Scholze For transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories. Akshay Venkatesh For his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects. The Web page is here.