The Continuum Hypothesis (CH) was introduced by Georg Cantor in 1878 and asserts that there is no infinite set of real numbers with size strictly between those of the natural numbers and the whole real line. Proving or disproving CH then became one of the first problems in set theory, and the techniques developed to solve that problem are now foundational to the field. In this talk we will discuss the method of forcing, and how it can be used to prove that CH is in fact independent of the ZFC axioms. No prior knowledge of set theory or forcing will be assumed or required.