The field of phylogenetic inference has undergone a profound transformation through the integration of advanced information technology, evolving from traditional morphological classification systems to sophisticated computational frameworks capable of processing genomic-scale datasets. This comprehensive review examines the historical trajectory of computational phylogenetics, tracing its development from Linnaeus's taxonomic foundations through the molecular revolution to contemporary phylogenomic approaches. We analyse the central methodological debates that have shaped the discipline, including the tension between parsimony and likelihood-based methods, the challenges of model selection in complex evolutionary scenarios, and the ongoing integration of machine learning techniques. The article presents a systematic mathematical framework for understanding key phylogenetic algorithms, accompanied by computational implementations that demonstrate their practical applications. Current obstacles in the field are critically evaluated, including the computational complexity of large-scale analyses, systematic errors in phylogenomic inference, and the challenges of accommodating complex evolutionary processes such as horizontal gene transfer and hybridisation. Through examination of both historical developments and contemporary challenges, this review provides insights into future directions for computational phylogenetics, emphasising the potential of hybrid approaches that combine traditional statistical methods with emerging artificial intelligence techniques. The analysis reveals that whilst significant progress has been achieved in computational efficiency and methodological sophistication, fundamental challenges remain in accurately reconstructing evolutionary relationships from increasingly complex datasets.
Richard Montgomery (Tue,) studied this question.