The Honourable Company of Edinburgh Golfers holds the claim of being the oldest verifiable organised golf club in the world, although the game of golf itself is several centuries older. The club's records date continuously back to 1744. That year, the club requested a silver club from the Edinburgh City Council as a competition trophy. The Council agreed. The Company drew up thirteen Rules of Golf for its first competition - rules that still underpin the modern game. The first competition was held over the five holes at Leith Links and won by John Rattray, who signed the rules and became the first club captain. The club played at Leith for nearly a century, until overcrowding forced a move in 1836 to the nine-hole Old Course at Musselburgh Links. Musselburgh's course, like St Andrews, was a public course - which eventually became too crowded for the Company's tastes. In 1891 the Company built its own private eighteen-hole course at Muirfield and took the Open Championship with it. This caused considerable bitterness in Musselburgh, which lost the right to host the Open. Old Tom Morris designed the new course. The first Open held at Muirfield in 1892 was the first major tournament anywhere contested over four rounds, or seventy-two holes.

Muirfield has an unusual layout for a links course. Most links courses run along the coast and then back again, giving you two sets of nine holes facing roughly the same direction - so a wind from one quarter punishes one nine and helps the other. Muirfield does something different. It is arranged as two loops of nine, one running clockwise and the other anti-clockwise, with no more than three consecutive holes ever facing the same direction. This means that on any given day, with the wind blowing steadily from one quarter, virtually every hole on the course presents a different apparent wind direction from the tee. Players cannot settle into a rhythm of into-wind or downwind shots. The course continually re-orients them. The course borders Archerfield Wood, which features in Robert Louis Stevenson's short story 'The Pavilion on the Links.' The course has been extended by 211 yards since the 2002 Championship to 7,245 yards.

Sixteen Open Championships have been won at Muirfield, the most recent in 2013 by Phil Mickelson. The roll of winners includes Harold Hilton, Harry Vardon, Walter Hagen, Alf Perry, Henry Cotton, Gary Player, Jack Nicklaus, Lee Trevino, Tom Watson, Nick Faldo (twice), and Ernie Els. Nicklaus won his first Open at Muirfield in 1966 - the victory that completed the first of his three career grand slams. He named his championship course and community at Dublin, Ohio, after the place: Muirfield Village, opened in 1974, has hosted his Memorial Tournament since 1976. Muirfield has also halted two post-war attempts at the calendar-year grand slam. In 1972, Nicklaus came to the Open having won that year's Masters and US Open; Lee Trevino beat him by a stroke. In 2002, Tiger Woods arrived with the same two majors in hand and ran into gale-force winds and rain in the third round - he shot 81 in the storm, rallied with a 65 on Sunday, and finished at even-par, six strokes outside the playoff. Muirfield also hosted the Ryder Cup in 1973, the 1959 and 1979 Walker Cups, the 1952 and 1984 Curtis Cups, ten Amateur Championships, and the Senior British Open from 2007.

Until 2017, women were barred from membership of The Honourable Company of Edinburgh Golfers, though they were permitted to play the course as guests. The exclusion was controversial. In May 2016 the club balloted on whether to admit women members. The vote produced a majority in favour, but not the two-thirds supermajority the club's rules required for change. The R&A, which runs the Open Championship, responded by removing Muirfield from the Open rotation. The club's secretary Stuart McEwen called the outcome 'a blow to the club, the local community and Scotland.' The public backlash and the loss of the Open prompted a re-ballot. In March 2017 the club voted again, this time meeting the supermajority requirement, and women were admitted to membership for the first time in the Company's 273-year history. In August 2022 Muirfield hosted the Women's British Open for the first time. The course that once hosted only men's championships now hosts every major women's championship the British game offers.

Muirfield sits at 56.042 degrees north, 2.821 degrees west, on the southern shore of the Firth of Forth in East Lothian, about a mile north-east of Gullane village. From above, the course's distinctive two-loop layout is visible - an outer ring of nine holes running clockwise around an inner ring of nine holes running anti-clockwise, with no two adjacent fairways quite facing the same direction. The clubhouse sits roughly in the centre. Best viewed from 2,000 to 3,500 feet for the full geometry. Nearest ICAO airport: Edinburgh (EGPH) ~22 nm west. Aberlady Bay opens to the south-west; the Firth of Forth extends to the north, with the Fife coast visible across the water. North Berwick Law - a sharp volcanic plug - rises 4 nm to the east. Three other golf courses (Gullane Numbers 1, 2 and 3, plus Luffness) lie immediately to the west and south-west; this whole stretch of dunes is golf country.