This paper provides a theoretical study on Multi-Objective Heuristic Search. We first classify states in the state space into must-expand, maybe-expand, and never-expand states and then transfer these definitions to nodes in the search tree. We then formalize a framework that generalizes A* to Multi-Objective Search. We study different ways to order nodes under this framework and their relation to traditional tie-breaking policies and provide theoretical findings. Finally, we study and empirically compare different ordering functions.