This article surveys the development of the economic theory of allianc
es over the last quarter of a century since the 1966 article by Olson
and Zeckhauser. The pure public good model and the joint product model
are presented and then brought up to date. Alternative demand functio
ns for military expenditures are indicated. Issues that concern allian
ce size, burden sharing, and suboptimality are addressed for the alter
native paradigms. Theoretical extensions are reviewed and have involve
d the technology of public supply, the security function, alternative
cost structures, group allocation processes, and institutional arrange
ments. Finally, theoretical developments are briefly related to the la
rge empirical literature.