Evolution can be predicted in the short term from a knowledge of selection and inheritance. However, in the long term evolution is unpredictable because environments, which determine the directions and magnitudes of selection coefficients, fluctuate unpredictably. These two features of evolution, the predictable and unpredictable, are demonstrated in a study of two populations of Darwin's finches on the Galápagos island of Daphne Major. From 1972 to 2001, Geospiza fortis (medium ground finch) and Geospiza scandens (cactus finch) changed several times in body size and two beak traits. Natural selection occurred frequently in both species and varied from unidirectional to oscillating, episodic to gradual. Hybridization occurred repeatedly though rarely, resulting in elevated phenotypic variances in G. scandens and a change in beak shape. The phenotypic states of both species at the end of the 30-year study could not have been predicted at the beginning. Continuous, long-term studies are needed to detect and interpret rare but important events and nonuniform evolutionary change.