"Cliffs of Dover" has endured as one of Johnson's best-known songs and is a mainstay at his concerts. It was ranked No. 17 in a list of "100 Greatest Guitar Solos" by Guitar World magazine, No. 34 in a list of "50 greatest guitar tones of all time" by Guitarist magazine, and remains a highly regarded staple within the guitar community.
Several other songs are dedicated to fellow guitarists: Johnson stated in a March 1990 interview with Guitar Player magazine that "Steve's Boogie" is dedicated to Austin-based pedal steel guitarist Steve Hennig, while "Song for George" is dedicated to an 80 year-old guitarist friend of his named George Washington. Furthermore, "East Wes" is dedicated to jazz guitarist Wes Montgomery, and takes its name from the 1966 album East-West by The Paul Butterfield Blues Band.
A DVD-Audio edition of Ah Via Musicom was released in 2002 through Capitol Records, but without Johnson's input. After he expressed disappointment in the sound quality and mixing, it was soon withdrawn by the label after 2500 copies were sold. In an August 2005 issue of Guitar Player, he confirmed that an authorized 5.1 DVD-Audio edition of the album was the works, but as of yet without a release date.
Robert Taylor at AllMusic gave Ah Via Musicom 4.5 stars out of five, praising Johnson for his "excellent chops and a clear tone" and describing the album as having "reached near-classic proportions within the guitar community."