This paper reviews research pertaining to the problem of speciation of the finches on the Galápagos archipelago carried out by assistants, several colleagues, Peter Grant and myself. I give a brief history of the radiation, examine the process of divergence by natural selection over time, and then consider the nature of the reproductive barrier to gene flow between closely related species. Fluctuating climatic conditions have produced a continuously changing ecological landscape and altered feeding conditions for the finches over the last 30 years. Finch populations tracked these changes by natural selection and evolutionary responses to the main events. At each event significant morphological change occurred from one generation to the next generation. As a consequence of these accumulated changes, the mean bill shape and body size of the Geospiza fortis and G. scandens populations differed markedly from 1973 to 2002. Song, a learned culturally transmitted trait, acted as a barrier to reproduction between these species. Rare incidences of misimprinting on song led to hybridization and introgression. Low levels of gene flow from one species to another increased genetic variation on which selection acted. Although the major driving force of diversification was ecological change, the process of diversification involved a subtle interplay between ecology, genetic evolution and learned culturally transmitted traits. An important message for conservation is that neither the environment nor species are fixed entities, therefore a wise strategy for conserving endangered species should keep them capable of further change.