The idea that birds and dinosaurs were closely related actually appeared fairly early on - Archaeopteryx had been named in 1861, two years after Darwin had published some book or other, and the first complete specimen was discovered later in the same year. From the same Solnhofen limestone, the little theropod Compsognathus had been known for a couple of years, and Thomas Huxley compared the two, concluding birds were obviously descendants of carnivorous dinosaurs.
There was some opposition to this idea at the time, and thinking on the origins of birds drifted for a while before more evidence was uncovered in the 1960s and 70s. By the end of the 70s the academic world had been convinced and the concept that birds were pretty much dinosaurs began to filter through to general public consciousness. The ash deposit finds at Liaoning in China in the 90s proved a real treasure trove and are still producing a string of important feathered dinosaur discoveries. I was at the Tucson trade fair when National Geographic's Archaeoraptor was bought by The Dinosaur Museum. The magazine were contacted and made a big splash with this supposed dinosaur-bird, which embarrassingly turned out to be two animals pieced together. The story had a happy ending, though, as a trip to the source turned up the other half to one of specimens - Microraptor - which in itself was hugely significant.
A recent find from the Solnhofen formation, the awkwardly titled Sciurumimus albersdoerferi, is the first theropod found with feathers that's not a close relative of birds. This seems to confirm suspicions that feathers were more than just the privilege of a certain group - coelurosaurs - and were more widely developed amongst theropods in general. There will be a lot more to learn about dinosaur feathers - as more are found, and as the techniques for studying them develop.