Tropical geometry is a broad collection of tools that translates questions in algebraic geometry into polyhedral combinatorics. For instance, subtle graph theoretic questions can be seen as reflections of the meromorphic function theory on a Riemann surface. The theory is motivated by ideas in mirror symmetry and high energy physics, and has begun to have a number of applications to much olderl questions. I will discuss the basic framework and ideas in the subject, as well as applications to Brill-Noether theory and enumerative geometry.