Free-radical acrylate polymerization is a very common example. As a new review paper states,
"[Oxygen] may react with primary initiating (R•) or propagating radicals (P-M•) to form peroxyl radicals (POO•), which are not energetically favorable toward initiating acrylate polymerization. These peroxyl radicals tend instead to terminate polymerization through radical−radical recombination (forming peroxide bridges, POOP) or by abstracting hydrogen from an adjacent molecule (POO• + RH → POOH + R•), where often the newly formed radical (R•) has insufficient reactivity toward the acrylate double bond to reinstate the initiation process."These issues are not a concern in traditional bulk polymerizations since the surface area contacting oxygen is very small, or the oxygen can easily be flushed from the reactor. For coatings on the other hand, the surface area becomes enormous and the impact of the inhibition - an uncured surface - cannot be ignored.
While the focus of the review paper is unnecessarily just on photoinitiated reactions (most of the schemes can be applied to any free-radical polymerization), the review does an excellent job of highlighting ALL the available options, covering both physical and chemical methods, including some options that I was previously unaware of such as the use of boranes and phosphines. This article will serve well as a reference for years to come.