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Philosophy of science
Thomas Kuhn (1922-1996) was an American physicist turned philosopher and historian of science. He is most noted for his concept of paradigm shifts set forth in The Structure of Scientific Revolutions, which resembles something like the concept of punctuated equilibrium if it were applied to intellectual history. This philosophy was not especially right as philosophies go, but it did cause a shake-up in philosophy of science which was only resolved by Imre Lakatos, who was completely right about everything.
Kuhn was not trained as a philosopher, and so his works take a rather "pop" view of how philosophy works; this makes them easy to read, but leaves them with a few pressing problems of style. If you want to put him in a box, he was an early post-structuralist. It's possible that, had Kuhn written some five or ten years later, his works would have been swept away in the anti-poststructuralist backlash of the late 1970s and early 1980s.
Overview of the philosophy
Prior to beginning, it should be noted that Kuhn was generally a pro-science kind of guy. Summarising his ideas like this makes him look a fair bit more anti-science than he was, because it's picking out all of the most dramatic phrases. Kuhn was not anti-science, but he was against the strict falsificationism which was the dominant philosophy of science at the time he was writing.
Kuhn started his academic career at a time when Karl Popper's ideas about falsification were extremely popular. However, he noticed that science often didn't progress exactly as Popper described. One of his key examples was the precession of the planet Mercury. It was discovered in 1859 that the precession of this planet (basically, the rotation of the ellipse of its orbit) defies that which is predicted by Isaac Newton's laws of gravitation and motion. If the precession of Mercury was driven solely by Newtonian mechanics, the precession would be 1.5436° per earth century, as opposed to the measured value of 1.5556° per earth century.
However, physicists did not immediately ditch Newton's theories as Popper would have predicted, because Newton worked so well everywhere else. Instead, they came up with a bunch of ad hoc explanations to keep everything working in a Newtonian way. It eventually turned out when Albert Einstein came along that Mercury moves fast enough to experience relativistic effects, distorting space-time and causing the extra precession. In other words, physicists spent 50 years behaving in an extremely non-Popperian way, until they actually had a theory that would allow them to explain everything at once. Kuhn's philosophy was written from a historical rather than logical perspective, attempting to explain why scientists would stick to old theories even when they were technically falsified.
Kuhn's view of the progression of science
Kuhn begins by describing the state a research field is in before it hits upon a paradigm. He summarises it as "a condition in which all members practice science, but in which their gross product scarcely resembles science at all." Basically, every researcher has their own pet hypothesis about how X works, and because nobody can agree upon X, they cannot make overall progress. His key example here is early electrodynamics, where the various different researchers spent most of their time arguing about whether electricity was a fluid, a force, or the work of gnomes.
Kuhn states that a hypothesis will develop into a paradigm when one of two conditions are met; either the hypothesis solves a major problem which has plagued the field, or the hypothesis develops an extra-shiny piece of new technology. In electrodynamics, this was the Leyden jar, an early capacitor which the electricity-as-a-fluid people claimed could capture the electrical fluid. Indeed, the electricity-as-a-fluid idea was a very successful paradigm, until science developed a better understanding of atoms and realised that it was the electrons all along.
Misuse by postmodernists and pseudoscience promoters
Because Kuhn argued that scientific progress is in some ways constrained by cultural, technological, etc. factors, his work is often misinterpreted to mean "everything's made up and the points don't matter." In response to charges of relativism, Kuhn added a postscript to the second edition of SSR. He noted that while he believed that while science isn't completely progressive, there are ways to test paradigms against current data such that their chronological order and usefulness in problem-solving could be determined. As Kuhn wrote: "That is not a relativist's position, and it displays the sense in which I am a convinced believer in scientific progress." If you're looking for someone who thinks there is absolutely no means of demarcating legitimate scientific methodology, Paul Feyerabend is your guy.
- Actually, every planet experiences these relativistic effects, but Mercury is the only one where they're substantial enough to be observed with 19th-century technology.
- Postscript: Revolutions and Relativism in SSR