Burnside was born in Harmontown, Mississippi, in Lafayette County, United States. He spent most of his life in North Mississippi, working as a sharecropper and a commercial fisherman, as well as playing guitar in juke joints and bars. He was first inspired to pick up the guitar in his early twenties, after hearing the 1948 John Lee Hooker single, "Boogie Chillen". Burnside learned music largely from Mississippi Fred McDowell, who lived nearby in an adjoining county. He also cited his cousin-in-law, Muddy Waters, as an influence.

Burnside grew tired of sharecropping and moved to Chicago in 1944 in the hope of finding better economic opportunities. He did find jobs at metal and glass factories, had the company of Muddy Waters and married Alice Mae in 1949, but things did not turn out as he had hoped. Within the span of one year his father, two brothers, and uncle were all murdered in the city, a tragedy that Burnside would later draw upon in his work, particularly in his interpretation of Skip James's "Hard Time Killing Floor" and the talking blues "R.L.'s Story", the opening and closing tracks on Burnside's 2000 album, Wish I Was In Heaven Sitting Down.

Around 1959, he left Chicago and went back to Mississippi to work the farms and raise a family. He killed a man at a dice game and was convicted of murder and sentenced to six months' incarceration (in Parchman Prison). Burnside's boss at the time reputedly pulled strings to keep the murder sentence short, due to having need of Burnside's skills as a tractor driver. Burnside later said "I didn't mean to kill nobody ... I just meant to shoot the sonofabitch in the head. Him dying was between him and the Lord."

His earliest recordings were made in the late 1960s by George Mitchell and released on Arhoolie Records. Another album of acoustic material was recorded that year and little else was released before Hill Country Blues, in the early 1980s. Recorded between 1980 and 1984 by Leo Bruin in Groningen, Netherlands. An album's worth of singles followed, released on ethnomusicology professor Dr. David Evans' High Water record label in Memphis, Tennessee.

In the 1990s, he appeared in the film Deep Blues and began recording for the Oxford, Mississippi, label Fat Possum Records. Founded by Living Blues magazine editor Peter Redvers-Lee and Matthew Johnson, the label was dedicated to recording aging North Mississippi bluesmen such as Burnside and Junior Kimbrough.

Burnside remained with Fat Possum from that time until his death, and he usually performed with drummer Cedric Burnside, his grandson, and with his friend and understudy, the slide guitarist Kenny Brown, with whom he began playing in 1971 and claimed as his "adopted son."

In the mid 1990s, Burnside attracted the attention of Jon Spencer, the leader of the Jon Spencer Blues Explosion, touring and recording with this group and gaining a new audience in the process.

Burnside's 1996 album A Ass Pocket of Whiskey (recorded with Jon Spencer) gained critical acclaim, earning praise from Bono and Iggy Pop. During this time he also provided the entertainment at private events such Richard Gere's birthday party.

After the death of Kimbrough and the burning of Kimbrough's juke joint in Chulahoma, Mississippi, Burnside quit recording studio material for Fat Possum, though he did continue to tour. After a heart attack in 2001, Burnside's doctor advised him to stop drinking; Burnside did, but he reported that change left him unable to play.

Members of his large extended family continue to play blues in the Holly Springs area: grandson Cedric Burnside tours with Kenny Brown and most recently with Steve 'Lightnin' Malcolm as part of the 'Juke Joint Duo', while his son Duwayne Burnside has played guitar with the North Mississippi Allstars (Polaris; Hill Country Revue with R. L. Burnside). Youngest son Garry Burnside used to play bass guitar with Junior Kimbrough and in 2006 released an album with Cedric. In 2004, the Burnside sons opened Burnside Blues Cafe, located 30 miles southeast of Memphis at the intersection of U.S. Highway 78 and Mississippi Highway 7 in Holly Springs.

Burnside had been in declining health since heart surgery in 1999. He died at St. Francis Hospital in Memphis, Tennessee on September 1, 2005 at the age of 78. Services were held at Rust College in Holly Springs, which is also where services were held for his friend, Junior Kimbrough, who died in 1998, with burial in the Free Springs Cemetery in Harmontown. Around the time of his death, he resided in Byhalia, Mississippi and his immediate survivors included:

Burnside had a powerful, expressive voice and played both electric and acoustic guitar, with and without a slide. His drone-heavy style was more characteristic of North Mississippi hill country blues than Delta blues. Like other country blues musicians, he did not always adhere to strict 12- or 16-bar blues patterns, often adding extra beats to a measure as he saw fit. He referred to this rhythmic eccentricity as "Burnside style" and recommended that backing musicians familiarize themselves with his style before playing along.

As was the case with his first role model John Lee Hooker, Burnside's earliest recordings sound quite similar to one another, even repetitive, in vocal and instrumental styling. Many of these songs eschew traditional chord changes in favor of a single chord or a simple bassline pattern that repeats throughout. Burnside played the guitar fingerstyle—without a pick—and often in open-G tuning. His vocal style is characterized by a tendency to "break" briefly into falsetto, usually at the end of long notes.

Like his contemporary T-Model Ford, Burnside favored a stripped-down approach to the blues, marked by a quality of rawness, and portrayed himself as a lifelong hard-drinking man singing songs of swagger and rebellion. Burnside collaborated in the late 1990s with The Jon Spencer Blues Explosion on the album A Ass Pocket of Whiskey; he consequently gained the attention of the alternative rock audience and was later cited as an influence by Hillstomp and covered on record by The Immortal Lee County Killers. Burnside's fellow Fat Possum musicians The Black Keys also credit him as an influence and interpolated his "Skinny Woman" into their track "Busted" .

Burnside knew many toasts—African American narrative folk poems such as "Signifying monkey" and "Tojo Told Hitler"—and fondly recited them between songs at his concerts and on recordings.