"Down by the River" is a song composed by Neil Young. It was first released on his 1969 album with Crazy Horse, Everybody Knows This Is Nowhere. 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.

The lyrics are apparently about someone who kills his lover by shooting her, like a murder ballad, or in the tradition of the mid-60s song "Hey Joe." The reason he gives for the killing is that she takes him to emotional heights from which he cannot bear to go on. Young has provided multiple explanations for the lyrics. In an interview with Robert Greenfield in 1970 Young claimed that "there's no real murder in it. It's about blowing your thing with a chick. It's a plea, a desperate cry." Introducing the song in New Orleans on September 27, 1984 Young claimed that it depicts a man "who had a lot of trouble controlling himself" who catches his woman cheating on him, then meets her down by the river and shoots her. According to Young, the local sheriff comes to the man's house and arrests him a few hours later.

"Down by the River" begins with electric guitars followed by bass guitar and snare drum before the vocals begin. The vocal sections are taken at a slow tempo. There are long instrumental passages after each of the first two refrains, during which Young plays short, staccato notes on his guitar and incorporates distortion. The song is composed in the key of E minor. The verse follows a chord progression of Em7-A while the pre-chorus is Cmajor7-Bm-Cmajor7-Bm-C-Bm-D and the chorus is G-D-D-A.

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