Young explained the context of the story in the liner notes of his 1977 anthology album Decade, stating that he wrote "Down by the River," "Cinnamon Girl" and "Cowgirl in the Sand" while delirious in bed in Topanga Canyon with a 103 °F (39 °C) fever.

"[9] Rolling Stone critic Rob Sheffield called "Down by the River" and "Cowgirl in the Sand" the "key tracks" on Everybody Knows This is Nowhere, calling them "long, violent guitar jams, rambling over the nine-minute mark with no trace of virtuosity at all, just staccato guitar blasts sounding as though Young is parachuting down into the middle of the Hatfield-McCoy feud.

"[11] Brett Milano of udiscovermusic.com rated Young's guitar solo as one of the 100 all-time greatest, stating that "it begins with almost nothing – the pure menace of one note played again and again – and builds to a pile of hulking riffs.

At the Rock Am Ring in Germany in 2002, Young, backed by Booker T Jones, Donald "Duck" Dunn, and Frank Sampedro, played "Down by the River" for over 27 minutes.

[13] At Farm Aid 1998, Young joined Phish—who headlined that year's festival—during the band's jam out of "Runaway Jim", leading them into a 20-minute version of "Down by the River".

In 2016, Neil Young and Promise of the Real played a 36+ minute version of the song to open their set at the Beale Street Music Festival in Memphis, Tennessee.

The Meters, The String Cheese Incident, Dave Matthews Band, Inner Circle, Low/Dirty Three, Tall Firs, McKendree Spring, Michael McDonald, The Mother Hips, The Sheepdogs, Puss n Boots, Norman Whitfield & The Undisputed Truth, Buddy Miles and Griffin also cover this song.

An acoustic version by the Indigo Girls appeared on their 1995 live double CD 1200 Curfews; the song had been a staple of their early 1993 shows and featured a cello and violin solo by Jane Scarpantoni and Scarlet Rivera respectively.

Singer/musician Norah Jones was joined onstage by Neil Young for an acoustic version of "Down by the River" on Day 2 of the 2014 Bridge Benefit concert.