Ludwig von Mises called gratuitous credit, the ability banks have to create new credit, the chief problem in a theory of banking. This paper traces how Mises and succeeding generations of Austrian-school economists have grappled with this problem, but have failed to find resolution. The result is that Austrian economists disagree on a variety of issues in banking and business cycle theory, such as whether there is an endogenous business cycle under free banking, or cycles only occur under central banking. Before a resolution can be attempted, current thinking must be clarified. This paper divides Austrian economists into five schools of thought. It points to a possible resolution in the economic development writings of Joseph Schumpeter.