Admissible set theory is, in a sense, the intersection of model theory, recursion theory, and set theory. From the set theory point of view they provide models of important fragments of ZFC. From the recursion theory point of view they provide a very strong generalization of the notion of finite. And from the model theory point of view they provide a way in which to see that L_{omega_1, omega} is a generalization of first order logic that preserves many of first order logics nice properties. In this talk we will be focusing on the model theoretic aspects of admissible sets. Specifically we will introduce admissible sets and their connection to the logic L_{omega_1, omega}. We will then review the model existence theorem and use it to prove two of the most important results concerning L_{omega_1,omega}, the completeness theorem and Barwise compactness. These two results show that, when viewed through the lens of admissible sets, L_{omega_1,omega} is a good generalization of first order logic.