We would like to believe that early in the new millennium the practice of conceptual modeling will rest on a sounder theory base than it does at present. Although a great deal of valuable research in information systems and conceptual modeling has been done during the last twenty years or so, the results in many cases have not yet sufficiently influenced other research work or found their way into current practice. Reasons for this might include the inaccessibility of much of the work and the time pressures on practising analysts. We think that inadequate consolidation of reported results is also a factor. Without consolidation, it is difficult to obtain an overall picture in a short time, and it can be hard to see the value of individual contributions. While it is easy to see the need for consolidation, achieving it is harder. Reviews and surveys can help, but do not by themselves provide the necessary linking of individual research efforts into some larger framework. This chapter draws on theories from philosophy, linguistics, cognitive science, conceptual modeling and information systems in order to develop such a framework. Its goals include improving our understanding of conceptual modeling as a process and relating the different representations of concepts that can occur during conceptual modeling. To illustrate some of its benefits, the framework is applied to the case of object-role modeling in its intended use as a conceptual modeling method and notation at the ontological level of a universe of discourse. The framework is applicable to other modeling methods and notations that may view the universe of discourse at a different level (e.g., epistemological). It assists analysts assessing and working with the techniques that have emerged in the late twentieth century. It provides the sound theory base we need for the new millennium.