What should a quantitative model of masking look like and why would we want it?

Quantitative models of backward masking appeared almost as soon as computing technology was available to simulate them; and continued interest in masking has lead to the development of new models. Despite this long history, the impact of the models on the field has been limited because they have fundamental shortcomings. This paper discusses these shortcomings and outlines what future quantitative models should look like. It also discusses several issues about modeling and how a model could be used by researchers to better explore masking and other aspects of cognition.