Discovery
Asymptotic freedom was discovered in 1973 by David Gross and Frank Wilczek, and by David Politzer. Although these authors were the first to understand the physical relevance to the strong interactions, in 1969 Iosif Khriplovich discovered asymptotic freedom in the SU(2) gauge theory as a mathematical curiosity, and Gerardus 't Hooft in 1972 also noted the effect but did not publish. For their discovery, Gross, Wilczek and Politzer were awarded the Nobel Prize in Physics in 2004.
The discovery was instrumental in rehabilitating quantum field theory. Prior to 1973, many theorists suspected that field theory was fundamentally inconsistent because the interactions become infinitely strong at short distances. This phenomenon is usually called a Landau pole, and it defines the smallest length scale that a theory can describe. This problem was discovered in field theories of interacting scalars and spinors, including quantum electrodynamics, and Lehman positivity led many to suspect that it is unavoidable. Asymptotically free theories become weak at short distances, there is no Landau pole, and these quantum field theories are believed to be completely consistent down to any length scale.
While the Standard Model is not entirely asymptotically free, in practice the Landau pole can only be a problem when thinking about the strong interactions. The other interactions are so weak that any inconsistency can only arise at distances shorter than the Planck length, where a field theory description is inadequate anyway.
Read more about this topic: Asymptotic Freedom
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