The duality between "niche" and "biotope" proposed by G. Evelyn Hutchinson provides a powerful way to conceptualize and analyze biogeographical distributions in relation to spatial environmental patterns. Both Joseph Grinnell and Charles Elton had attributed niches to environments. Attributing niches, instead, to species, allowed Hutchinson's key innovation: the formal severing of physical place from environment that is expressed by the duality. In biogeography, the physical world (a spatial extension of what Hutchinson called the biotope) is conceived as a map, each point (or cell) of which is characterized by its geographical coordinates and the local values of n environmental attributes at a given time. Exactly the same n environmental attributes define the corresponding niche space, as niche axes, allowing reciprocal projections between the geographic distribution of a species, actual or potential, past or future, and its niche. In biogeographical terms, the realized niche has come to express not only the effects of species interactions (as Hutchinson intended), but also constraints of dispersal limitation and the lack of contemporary environments corresponding to parts of the fundamental niche. Hutchinson's duality has been used to classify and map environments; model potential species distributions under past, present, and future climates; study the distributions of invasive species; discover new species; and simulate increasingly more realistic worlds, leading to spatially explicit, stochastic models that encompass speciation, extinction, range expansion, and evolutionary adaptation to changing environments.