Inference of phylogenetic (evolutionary) trees comprising hundreds or thousands of organisms based on the maximum likelihood criterion is a computationally extremely intensive task. This paper describes the evolution of the AxML program family which provides novel algorithmic as well as technical solutions for the maximum likelihood-based inference of huge phylogenetic trees. Algorithmic optimizations and a new tree building algorithm yield runtime improvements of a factor greater than 4 compared with fastDNAml and parallel fastDNAml, returning equally good trees at the same time. Various parallel, distributed, and Grid-based implementations of AxML give the program the capability to acquire the large amount of required computational resources for the inference of huge high-quality trees. Copyright © 2004 John Wiley & Sons, Ltd.