Brill-Noether theory is the study of algebraic curves and their maps to projective space. A series of results in the 80's describe the Brill-Noether theory of sufficiently general curves. More recently, many researchers have become interested in the Brill-Noether theory of special curves -- if a curve admits one unusual map to projective space, what does that imply about the existence and behavior of other such maps? We will begin with a gentle introduction to this field of study, and then survey some of the recent results on special curves. We will conclude with recent results on etale double covers of curves -- a subject known as Prym-Brill-Noether theory -- and a surprising relation to the combinatorics of Coxeter groups.