Phylogeny reconstruction from molecular data poses complex optimization problems: almost all optimization models are NP-hard and thus computationally intractable. Yet approximations must be of very high quality in order to avoid outright biological nonsense. Thus many biologists have been willing to run farms of processors for many months in order to analyze just one dataset. High-performance algorithm engineering offers a battery of tools that can reduce, sometimes spectacularly, the running time of existing phylogenetic algorithms. We present an overview of algorithm engineering techniques, illustrating them with an application to the "breakpoint analysis" method of Sankoff et al., which resulted in the GRAPPA software suite. GRAPPA demonstrated a million-fold speedup in running time (on a variety of real and simulated datasets) over the original implementation. We show how algorithmic engineering techniques are directly applicable to a large variety of challenging combinatorial problems in computational biology.