Abstract: This talk will be a survey of literature about the Galois action on exceptional curves on del Pezzo surfaces. We will begin by discussing the permutation of the 27 lines on a cubic surface and giving examples. Other examples are the 28 bitangents on a quartic plane curve and the 240 (-1)-curves on a degree 1 del Pezzo surface. The story will reference work by Carter, Corn, Elsenhans-Jahnel, Kulkarni, Shioda, and Varilly-Alvarado.