The paradox of slums is that despite the wealth and the high level of economic development of the United States, they are as prevalent in our cities as in many an overseas urban area. Assuming that slums do have a function in the development of the city, the chapter looks at how this function evolves and shows its direct relation to the growth of the city. To illustrate the complexity of slum formation and to attempt a theory of slum growth which correlates with a theory of city growth, it is useful to construct a simple model. The chapter outlines theory in the hope that unemotional thinking about slum formation may provide an ultimate solution. In short, slum formation depends on the rate of in-migration as well as on the rate of integration or absorption of the migrants. Obviously, too, slum formation depends on the existence of barriers to escalation as well as distinction between income and "ability" classes.