This document presents hypotheses about how much understanding a user needs to perform skillfully using a computer or a computer program. A framework for characterizing user understanding is presented which includes three criteria for evaluating the representation generated during problem solving: (1) internal coherence--whether the components of the user's knowledge are related in an integrated structure; (2) validity--whether the user's knowledge accurately reflects the behavior of the device; and (3) integration--the extent to which the user's knowledge about a device is tied to other components of a user's knowledge. Each criterion is defined, discussed in detail, and illustrated by examples. The summary reiterates the multi-dimensional quality of understanding and argues that the degree of internal coherence, validity, and integration does not depend on a single aspect of knowledge, but upon several. It is stressed that a user should not be considered as either performing with or without understanding, since it is possible for the user to have acquired some components of knowledge and not others. Lists of 33 references and 41 publications written by people in the Institute for Cognitive Science complete the document. (JB)