This chapter is dedicated to two fundamental notions in general second order potential theories. Duality is reviewed first with its important consequence of reformulating \({\mathcal F}\) -superharmonics as subharmonics for a dual subequation \(\widetilde {\mathcal F}\) . Next, the unifying notion of monotonicity is reviewed. Together, they give rise to the duality-monotonicity method for proving the validity of the comparison principle, which is a key ingredient in the treatment of existence and uniqueness of solutions to the Dirichlet problem for \({\mathcal F}\) -harmonic functions.