 There are really two kinds of approaches to new axioms—the local approach and the global approach. On the local approach one seeks axioms that answer questions concerning a specifiable fragment of the universe, such as Vω+1 or Vω+2, where CH lies. On the global approach one seeks axioms that attempt to illuminate the entire structure of the universe of sets. The global approach is clearly much more challenging. In this entry we shall start with the local approach and toward the end we shall briefly touch upon the global approach. 