abstract: The purpose of this talk is to explain how to give a geometric explanation of all the known Harnack inequalities for the Ricci flow (including the estimates by Hamilton and Brendle), and also how to obtain an effective method to generate new ones. The main technical tool we need for such a goal is the notion of Canonical Expanding Soliton, which is roughly a special kind of space-time gradient soliton in a certain limiting sense.