Current results on the asymptotics of dynamo models

Magnetic field generation and evolution models that are capable of describing a large body of observational material are currently available for different celestial bodies. Despite recent decades of great success in numerical magnetic hydrodynamics and in detailed research into some specific problems, asymptotic methods still have to be used to clarify the magnetic field generation mechanism in dynamo theory. In this review, current asymptotic methods are presented together with the results of their application to the simulation of solar, stellar, and galactic magnetic activities.