A Fuchsian group \Gamma has a modular embedding if its adjoint trace field is a totally real number field and every unbounded Galois conjugate \Gamma^\sigma comes equipped with a holomorphic (or conjugate holomorphic) map {\phi^\sigma : \mathbb{B}^1 \to \mathbb{B}^1} intertwining the actions of \Gamma and \Gamma^\sigma on the Poincaré disk \mathbb{B}^1. I will describe why these should be rare and special, the previously-known examples (coming from triangle groups and Teichm\'uller curves), and my recent construction of the first cocompact nonarithmetic Fuchsian groups with a modular embedding that are not commensurable with a triangle group.