Many practical planning problems necessitate the generation of a plan under incomplete information about the state of the world. In this paper we propose the notion of Assumption- Based Planning. Unlike conformant planning, which attempts to find a plan under all possible completions of the initial state, an assumption-based plan supports the assertion of additional assumptions about the state of the world, often resulting in high quality plans where no conformant plan exists. We are interested in this paradigm of planning for two reasons: 1) it captures a compelling form of commonsense planning, and 2) it is of great utility in the generation of explanations, diagnoses, and counter-examples - tasks which share a computational core with planning. We formalize the notion of assumption-based planning, establishing a relationship between assumption-based and conformant planning, and prove properties of such plans. We further provide for the scenario where some assumptions are more preferred than others. Exploiting the correspondence with conformant planning, we propose a means of computing assumption-based plans via a translation to classical planning. Our translation is an extension of the popular approach proposed by Palacios and Geffner and realized in their T0 planner. We have implemented our planner, A0, as a variant of T0 and tested it on a number of expository domains drawn from the International Planning Competition. Our results illustrate the utility of this new planning paradigm. Copyright © 2013, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.