In this talk, we start with the classical Hardy inequality. Then we define the p-Dirichlet integral with a potential and the p-Laplace equation with a potential. We review some fundamental concepts in criticality theory, such as Hardy-weights, criticality, subcriticality, supercriticality, null-sequences, and ground states, and an Agmon-Allegretto-Piepenbrink type theorem. After that, we present optimal Hardy-weights for the p-Dirichlet integral. We explain part of the proof after recalling some characterizations of criticality. In the end, we discuss further extensions including my current work.