Set theory has been concerned for a century with finding and studying the most fundamental mathematical axioms, and we now know that almost all of mathematics can be viewed as taking place within the Zermelo-Frankael ZFC axioms. These axioms, however, are actually quite weak, in the sense that there are many elementary questions that, provably, they do not settle. For example, the Continuum Hypothesis, the question of whether every uncountable set of real numbers is bijective with the set of all real numbers, is known to be independent of the ZFC axioms; it is neither provable nor refutable. This independence phenomena is ubiquitous, for we have found that many mathematical questions, including nearly all interesting questions in infinite combinatorics, are independent of the ZFC axioms. With Cohen's forcing technique, we canconstruct models of set theory where such principles are true and others where they are false. Because of this, the models of set theory themselves have become the fundamental object of study. In the latter part of this talk, I would like to consider a new forcing principle, the Maximality Principle, which asserts that any sentence holding in some forcing extension and all subsequent extensions, is already true. This principle is expressible in modal logic by the scheme $\lozenge\square\varphi\implies\varphi$, and is equivalent to the modal theory S5. I will prove that the Maximality Principle is relatively consistent with ZFC. Stronger versions of the scheme have a greater consistency strength, leading to surprisingly large cardinals.