In 1978, Dire Straits recorded their first album, Dire Straits (so called due to the financial condition the members were living in at the time), at Basing Street studios (now known as 'Sarm West') near Portobello Road in West London for £12,500.

During the initial U.K. release on Vertigo Records, a division of Phonogram, the album had little promotion and was not well received. However, the U.K. album came to the attention of Karin Berg, an assistant in the artists and repertoire (A&R) department of Warner Bros. Records in New York City.

She felt it was the kind of music that audiences were hungry for, but only one person in her department agreed at first. "Other people didn't hear it. The act was doing poorly in the U.K., and the record wasn't getting air play." After the album was released in the United States by Warner Brothers, it caught on quickly and sold over 1 million copies.

Later, when re-released as a single, "Sultans of Swing" became a surprise U.K. chart hit, making the top 10, and then went on to become a very popular live song throughout the band's career. The first album eventually went top 10 in every European country.

The group's second album, Communiqué, followed in 1979. Communiqué went to number one on the German album charts with Dire Straits simultaneously at number three. Singles released included "Lady Writer" and "Angel of Mercy". The album continued in a similar monochromatic vein as the first album, if somewhat more polished sonically. Within a year, however, this approach would change along with the band's lineup.

In 1980, Dire Straits released its third album, Making Movies. This marked a move towards more complex arrangements and production which would continue for the remainder of the band's career. The most successful chart single from the album was "Romeo and Juliet", while the album's opening track "Tunnel Of Love" (with its intro "The Carousel Waltz" written by Richard Rodgers and Oscar Hammerstein II), went on to become another live favorite.

Making Movies saw the departure of David Knopfler while the recording of the album was still in progress; Sid McGinnis filled in on rhythm guitar as the sessions continued. The album also featured keyboardist Roy Bittan from Bruce Springsteen's E Street Band and was produced by Knopfler with Jimmy Iovine.

Although Mark played on one track on his younger brother David's first solo album, the two men have not reconciled over the years.

Keyboardist Alan Clark and Californian guitarist Hal Lindes joined the lineup for the fourth studio album, Love over Gold, which was well received on its release in September 1982, and reached #1 in the United Kingdom. The title was inspired by graffiti seen from the window of Knopfler's old council flat in Deptford, SE London.

It was also the first Dire Straits album produced solely by Mark Knopfler. Its main chart hit, "Private Investigations", gave Dire Straits their first U.K. top 5 hit single, reaching the number two position despite its almost seven-minute length, and became one of the band's most popular live songs. In other parts of the world, the single "Industrial Disease" was the album's calling card, particularly in Canada where it became a top 10 hit. Love over Gold reportedly sold two million copies in the first six weeks of its release.

Shortly after the release of Love Over Gold, drummer Pick Withers left the band for a jazz career. His replacement was Terry Williams, formerly of Rockpile.

In 1983, a four-song EP titled ExtendedancEPlay was released. It featured the hit single "Twisting By the Pool" which reached the Top 20 in the UK. Dire Straits also embarked on a world tour. This was followed in 1984 by the double live album, Alchemy, a recording of two live concerts of the group at London's Hammersmith Odeon in June, 1983, and reportedly was released au naturel, with no studio overdubs on the live material. At the time, the concert was also issued on video.

During 1983 and 1984 Mark Knopfler was involved in other projects. He wrote the music score for the films Local Hero (released in 1983), and Cal (released in 1984), the original soundtracks to both of which became available immediately on album.

At the end of 1984 Dire Straits started recording tracks at Air Studios Montserrat for their fifth studio album, Brothers in Arms, released in 1985. There were further personnel changes, with the addition of a second keyboardist, Guy Fletcher.

Guitarist Hal Lindes left the band suddenly during the recording sessions. His place was taken by Jack Sonni although Sonni was not credited as an official band member for the new album release. American jazz fusion drummer Omar Hakim joined Terry Williams on drums: both are credited as band members for the album.

Brothers In Arms went on to become the biggest-selling album of 1985 in the United Kingdom, and was a huge hit internationally. It spawned several chart singles: "Money for Nothing" (which reached number one in the United States and number four in the United Kingdom), "So Far Away", "Brothers In Arms", "Walk of Life", and "Your Latest Trick".

The song "Money for Nothing" was the first video ever to be played on MTV in Britain, and featured guest vocals by Sting from The Police. It also won a Grammy for the Best Rock Performance by a Duo or Group with a Vocal in 1985 at the 28th annual Grammy Awards.

The album's title track is reported to be the world's first CD single. It was issued in the United Kingdom in two separate singles as a promotional item, one distinguished with a logo for the tour, Live in '85, and a second to commemorate the Australian leg of the tour marked Live in '86.

Containing just four tracks, it had a very limited print run. Meanwhile, "Walk of Life" was the band's most commercially successful single in the United Kingdom, peaking at number two. "Money for Nothing," "Walk of Life" and "Brothers In Arms" all went on to become regular live favorites.

The commercial success of Brothers in Arms was greatly aided by the fact that the album was one of the first fully digitally recorded and produced albums available in the then new Compact Disc format, leading early adopters of the new technology to consider it a "must buy" album in a limited landscape of available music in CD format. The Brothers in Arms CD was one of the first CD albums to contain material not found on the LP equivalent; it featured the full 12" version of the "Money for Nothing" cut, rather than the version that appears on the LP.

In fact, the CD includes extended versions of all tracks featured on side one of the original LP, with the exception of "Walk of Life". The new compact disc offered an excellent showcase for Knopfler's meticulous production values on the group's previous albums, leading many existing fans to repurchase the group's entire back catalogue.

The 1985–86 world tour which followed the album's release was phenomenally successful. While playing a 13-night residency at Wembley Arena, the band moved down the road to Wembley Stadium on the afternoon of July 13, 1985 to appear in Live Aid. Their set included "Money For Nothing" with Sting as guest vocalist. The tour ended at the Entertainment Centre in Sydney, Australia, where Dire Straits still holds the record for consecutive appearances (21 nights).

The last show of this extended stay in Sydney was recorded and broadcast on Australian and New Zealand television, and is well known for the one-off calypso rendition of "So Far Away" and the band's impromptu attempt at the famous Australian folk song "Waltzing Matilda". In a two-year span, Dire Straits played 247 shows in over 100 different cities.

Brothers in Arms was similarly successful in the United States, where it peaked at No. 1 on Billboard magazine's Top Pop Albums Chart for nine weeks, going multi-platinum, and finishing at No. 5 for 1986.

Brothers in Arms was certified nine times platinum in August 1996. In 2005 it was re-released in Super Audio CD format and DualDisc format, to mark the 20th anniversary since the album's original release. The 20th anniversary edition won a Grammy for Best Surround Sound Album. A recent poll conducted in the United Kingdom revealed that Brothers in Arms is the 5th best-selling album there of all time.