Thomas Grady Martin (January 17, 1929 – December 3, 2001) was an American session guitarist in country music and rockabilly.
A member of The Nashville A-Team, he played guitar on hits
such as Marty Robbins' "El Paso", Loretta Lynn's "Coal Miner's
Daughter" and Sammi Smith's "Help Me Make It Through the Night".
During a nearly 50-year career, Martin backed such names as Elvis Presley,
Buddy Holly, Johnny Burnette, Don Woody and Arlo Guthrie, Johnny Cash, Patsy
Cline and Bing Crosby. He is a
member of the Rockabilly Hall of Fame.

Grady Martin was born on January 17, 1929 in Chapel Hill,
Tennessee. He grew up on a farm with his oldest sister, Lois, his older
brothers, June and Bill, and his parents, Claude and Bessey; and had a horse he
named Trigger. His mother played the piano and encouraged his musical talent.
At age 15, Martin was invited to perform regularly on
WLAC-AM in Nashville, Tennessee, and made his recording debut two years later
on February 15, 1946 with Curly Fox and Texas Ruby in Chicago, Illinois.
That same year, he joined Paul Howard's Western
swing-oriented Arkansas Cotton Pickers as half of Howard's twin guitar ensemble
with Robert "Jabbo" Arrington and performed on the Grand Ole Opry.
When Howard left, Opry newcomer Little Jimmy Dickens hired several former
Cotton Pickers, including Martin, as his original Country Boys road band. He
later joined Big Jeff Bess and the Radio Playboys followed by a stint with the
Bailes Brothers Band.

It was as a session musician starting in the late 1950s that
Martin made his greatest mark on country and rockabilly music.
As a guitarist with The Nashville A-Team, he provided the guitar on the Marty Robbins hits "El Paso" (1959) and "Don't Worry" (1961), on Roy Orbison's "Oh, Pretty Woman" (1964) and Lefty Frizzell's "Saginaw, Michigan" (1964). His guitar work was also displayed in Johnny Horton's "The Battle of New Orleans" (1959) and "Honky Tonk Man" (1956), and especially his pure rockabilly sound on "I'm Coming Home" (1957). He shaped countless other classics, Brenda Lee's "I'm Sorry" and "Rockin'

Martin is credited with accidentally stumbling onto the
electric guitar "fuzz" effect during a recording session with
Robbins; his guitar was run through a faulty channel in a mixing console,
generating the fuzz sound on "Don't Worry".
The 1960s saw Martin move to the forefront of session
guitarists and also issue a pair of rock & roll instrumental singles,
"The Fuzz"/"Tippin' In" and "Big Bad Guitar." He
also found success as a songwriter with "Snap Your Fingers," which
was recorded in hit versions by Joe Henderson and Barbara Lewis and later
covered by Ronnie Milsap, among others.
In 1978, with his studio career over, Martin returned to the
life of a
touring musician; first with Jerry Reed and then as lead guitarist
for Willie Nelson's band, appearing in Nelson's 1980 film Honeysuckle Rose. In
1994, deteriorating health forced him to retire, but he produced Nelson's 1995
honky tonk album, Just One Love.

The Nashville Entertainment Association gave him its first
Master Award in 1983, and he was the 83rd inductee into the Rockabilly Hall of
Fame. On April 5, 2000, he received a Chetty award for significant instrumental
achievement at Nashville's Ryman Auditorium during the Chet Atkins Musician
Days festival. Health problems prevented Martin from attending; Nelson, Vince
Gill and Marty Stuart presented the award—named after Atkins, who attended—to
Martin's son, Joshua. Grady Martin was inducted into the Musicians Hall of Fame
in 2007.
Martin died from a heart attack on December 3, 2001 at the
Marshall Medical Centre in his hometown of Lewisburg, Tennessee; and was
interred at Hopper Cemetery in Marshall County, Tennessee. (Info edited mainly
from Wikipedia)
Here's classic footage of Red singing the old chestnut
"Crawdad Hole" with a stellar backing band--Grady Martin on
doubleneck Bigsby guitar, Bob Moore on bass, Tommy Jackson on fiddle, Bud
Isaacs on steel.