Like many songs from Murmur, "Perfect Circle" has a sound typified by unusual instruments and recording techniques. The song opens with Honky tonk piano, a style more associated with ragtime and early country music than the college rock scene of which R.E.M. was a member. Two pianos were recorded, and the slightly out-of-sync sound and reverb achieve a detached otherworldly effect. The song also features Peter Buck's 12 string guitar.

After R.E.M.'s drummer Bill Berry left the band in 1997 for personal reasons, the band began reintroducing "Perfect Circle" into their live performances and radio appearances to promote their then forthcoming album Up. During this time period, members of the band stated that the song was primarily written by Berry and dedicated their performance of it to him.

The lyrics of "Perfect Circle" are purposely opaque. Members of the band agree that the song has an emotional theme that can be interpreted in many ways. For guitarist Peter Buck, the song elicits images of children playing football one evening in Trenton, New Jersey. Singer Michael Stipe interprets the song as being about longing in a relationship. He also has stated that other interpretations are equally valid: "It was an intensely personal song to me. I really like that it can mean two different things. ... It's the exact same feeling, but the details are different." "A perfect circle of acquaintances and friends"...a theme in the song is a beautiful representation of what the song can be about.

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