Various approaches have recently been proposed to ease the manipulation of models for specific purposes (e.g., automatic model adaptation or reuse of model transformations). Such approaches raise the need for a unified theory that would ease their combination, but would also outline the scope of what can be expected in terms of engineering to put model manipulation into action. In this work, we address this problem from the model substitutability point of view, through model typing. We introduce four mechanisms to achieve model substitutability, each formally defined by a subtyping relation. We then discuss how to declare and check these subtyping relations. This work provides a formal reference specification establishing a family of model-oriented type systems. These type systems enable many facilities that are well known at the programming language level. Such facilities range from abstraction, reuse and safety to impact analyses and auto-completion.