"He was one of the last great blues guitar heroes. He was an electric God," said Gregg Parker, CEO and a founder of the Chicago Blues Museum.
Rush was placed at No 53 on the list of Rolling Stone's 100 greatest guitarists, the magazine describing him as "a gunslinging cross of Muddy Waters and BB King - as well as a knockout songwriter".
But for all the respect he garnered from his fellow musicians and the adoration of aficionados, Rush's career often faltered, and he never felt as if he had reached the level he wanted.
"I don't do nothin' but worry," he once said. "Yeah, that's about what I do, worry about my damn hard times and bills."
Rush was born in Philadelphia, Mississippi, on April 29, 1934, one of seven children. He worked on a sharecropping farm before moving to Chicago with his family when he was 14.
When he was still in his teens he saw Muddy Waters perform and took up the guitar in earnest, though as a left-hander he played a right-handed guitar upside down. He began going to clubs and practising at home, supporting himself by working in a steel mill and as a lorry driver.
Rush loved to play to live audiences, from small clubs on the West Side of Chicago to sold out venues in Europe and Japan.
"He was king of the hill in Chicago from the late 1950s into the 1970s and even the 80s as a live artist," said Bates.
But he got less national and international attention than some other blues musicians because he wasn't a big promoter.
Rush did not help himself, developing a reputation as an occasionally moody and erratic live performer, delivering a blistering set one night but lacklustre fare the next.
He was also scathing about the very notion of the "West Side Sound", remarking: "The public came up with this, not me. You know, they had the West Side, South Side and North Side. They started naming it Chicago blues. I don't know - Chicago blues, San Francisco, Los Angeles, New York. Who cares? It's blues, you know?"
Disillusioned by the many bumps in the road, in the late 1970s he retired from the business, but returned in 1985 with a US tour and a 1988 live album, Tops, recorded at the San Francisco Blues Festival. He never embraced the traditional rocker's lifestyle, however.
"He preferred to go out and play and go back and sleep in his own bed," said Bates. "He was not a show business guy."
Rush won a Grammy for Best Traditional Blues Recording in 1999 for Any Place I'm Going, and was inducted into the Blues Foundation Hall of Fame in 1984.
In one of his final appearances on stage at the Chicago Blues Festival in 2016, Rush watched beneath a black Stetson hat from a wheelchair as he was honoured by the city of Chicago, according to the Chicago Tribune.
He is survived by wife Masaki Rush, eight children and various grandchildren and great grandchildren.
- AP