Abstract: We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vladut to those with arbitrarily many recovery sets by exploiting the structure of fiber products of curves. Employing maximal curves, we create several new families of locally recoverable codes with multiple recovery sets. In addition, we consider the relationship between local error recovery and global error correction as well as the availability required to locally recover any pattern of a fixed number of erasures. This talk is based on joint work with Beth Malmskog (Colorado College) and Gretchen Matthews (Clemson University)