The Hodge conjecture claims that on a compact complex manifold X, the cohomology class of every harmonic (p,p) form can represented as a rational sum of the cohomology classes of subvarieties of X. This very dense statement suggests a deep connection between the analytic tool of forms and the geometric data of subvarieties on X. In this talk, we will focus primarily on unraveling the full statement of the Hodge conjecture, and discuss a few of the more accessible cases proven to date, including the Lefschetz (1,1) theorem.