Codensity monads provide a universal method to generate complex monads from simple functors. Recently, important monads in logic, denotational semantics, and probabilistic computation (such as ultrafilter monads, the Vietoris monad, and the Giry monad) have been presented as codensity monads, using complex arguments. We simplify these codensity presentations by proposing a unifying categorical approach, which only uses density (of functors) and duality (of categories). To sum up: "Codensity Monads = Density + Duality".