Savile row suits are the pinnacle of English style. They have a long history of great men's fashion. If you are ever in London, be sure to try to check them out.
Savile Row isn't a brand but rather a specific street in London where most of the most prestigious tailors and bespoke suitmakers gather. They started gathering there around 1800 as some of the city's best dressed men began gathering there. In the 1950s and 1960s, the group began working on modernising and staying with the increasing use of suits in business, casual, and leisure environments. In the late 1990s and early 2000s, the property market made rents on the street skyrocket, and pushed many makers to other locations. In addition, many Italian and other fashion house accused the London suitmakers of being too stodgy and behind the times.
Today there are about 30 or so tailors on the street, although the number fluctuates. Some of the more well-known makers include Gieves & Hawkes and Henry Poole. You'll see some men's fashion labels claim that they are "Savile Row" originated. In reality, to be from Savile Row you should have your suit measured and made on the street. While it can be argued that American and Italian makers have taken some of the swagger from the British market, its still THE place to go for bespoke suits.
Understand that Savile Row is not cheap. Expect to pay upwards of 2000 British pounds, or about $4000 plus for a basic bespoke setup.
If you don't have the time or cash to go to London, you can check them out on one of their road shows. The bigger tailors will often go to New York or San Francisco for a couple days. Definitely check their schedules and make an appointment, as even today they will be in high demand.