Order stars and stiff integrators

Order stars, introduced in G. Wanner, E. Hairer, S.P. Nørsett (Order stars and stability theorems, BIT 18 (1978) 475–489), have become a fundamental tool for the understanding of order and stability properties of numerical methods for stiff differential equations. This survey retraces their discovery and their principal achievements. We also sketch some later extensions and describe some recent developments.