In this talk I will discuss several toy models for biological evolution, all sharing two essential features: an asymptotically infinite population of individuals marked by “fitness” values assigned at birth, and elimination of individuals with lowest fitness. The main question we will consider is the asymptotic fitness landscape. The models include the Bak-Sneppen model, introduced as the first example for self-organized criticality, although this has not been proved rigorously, as well as several related more tractable models I have been working on in recent years.