"Eleanor Rigby" combines Paul McCartney's brand of lyrical imagery with a string octet (a conventional string quartet, doubled) arranged by George Martin under McCartney's direction. Both the lyrics and arrangement are a major departure from The Beatles' prior output.

Although Martin once pointed to Bernard Herrmann's score for Fahrenheit 451 as inspiration for the string arrangement, the film was not released until several months after the recording; Martin later stated he was thinking of Herrmann's score for Psycho. The compression and lack of reverberation given to the strings provides a stark, urgent sound that complements Martin's arrangement.

McCartney originated the song and the name, rejecting his initial choice, "Daisy Hawkins," in favour of a name derived from The Beatles' Help! costar Eleanor Bron and by Rigby & Evens, a wine shop McCartney noticed in Bristol. The fact that an actual person named Eleanor Rigby is buried in Liverpool's Woolton Cemetery is a bizarre coincidence. McCartney initially named the clergyman Father McCartney, but picked the name MacKenzie out of a phone book, out of concern that the character could be misinterpreted as being the writer's father.

"Eleanor Rigby" is one of the few songs with lyric contributions from all four Beatles. John Lennon laid claim to "40 percent" of the lyrics (which was later disputed), including the line "Wearing a face that she keeps in the jar by the door", though those present at the writing dispute Lennon's claim. Ringo Starr contributed the line "Father McKenzie, writing the words of a sermon that no-one will hear", and George Harrison provided the "Ah, look at all the lonely people" hook.

"Eleanor Rigby" was released as a double A-side (with "Yellow Submarine") concurrently with the album.

The Beatles' unfolding innovation in the recording studio reaches its apex with the album's final track. Lennon's "Tomorrow Never Knows" was one of the first songs in the emerging genre of psychedelic music, and included such groundbreaking techniques as reverse guitar, processed vocals and looped tape effects. Musically, it is drone-like, with a strongly syncopated, repetitive drum-beat. The lyrics were inspired by Timothy Leary's book, The Psychedelic Experience: A Manual Based on The Tibetan Book of the Dead, although the title itself was inspired by a Ringo Starr malapropism.

Much of the backing track consists of a series of prepared tape loops, stemming from Lennon's and McCartney's interest in and experiments with magnetic tape and musique concrète techniques at that time. According to The Beatles' session chronicler Mark Lewisohn, Lennon and McCartney prepared a series of loops at home, and these then were added to the pre-recorded backing track. This was reportedly done live in a single take, with multiple tape recorders running simultaneously, some of the longer loops extending out of the control room and down the corridor.

Lennon's processed lead vocal was another innovation. Always in search of ways to enhance or alter the sound of his voice, he gave a directive to EMI engineer Geoff Emerick that he wanted to sound like he was the Dalai Lama singing from the top of a high mountain. Emerick solved the problem by routing a signal from the recording console into the studio's Leslie speaker, giving Lennon's vocal its ethereal, filtered quality (Emerick was later reprimanded by the studio's management for doing this).

A key production technique used for the first time on this album was automatic double tracking (ADT), invented by EMI engineer Ken Townsend on 6 April 1966. This technique used two linked tape recorders to automatically create a doubled vocal track. The standard method was to double the vocal by singing the same piece twice onto a multitrack tape, a task Lennon particularly disliked. The Beatles were reportedly delighted with the invention, and used it extensively on Revolver. ADT quickly became a standard pop production technique, and led to related developments, including the artificial chorus effect.

Lennon's other contributions included "I'm Only Sleeping", "And Your Bird Can Sing", "She Said She Said" and "Dr. Robert".

On "I'm Only Sleeping", Harrison played the notes for the lead guitar (and for the second guitar in the solo) in reverse order, then reversed the tape and mixed it in. The backwards guitar sound has been said to "suspend the laws of time and motion to simulate the half-coherence of the state between wakefulness and sleep". The backwards guitar is mixed a little differently on the American version, which is not included on the American Revolver but on The Beatles Yesterday and Today.

According to Lennon, some of the lyrics of "She Said She Said" were taken almost verbatim from a conversation he had with actor Peter Fonda in August 1965, while he (Lennon), Harrison and Starr were under the influence of LSD at their rented house in Benedict Canyon (in Beverly Hills, California). During a conversation, Fonda said "I know what it's like to be dead," because as a boy he had almost died from a self-inflicted gunshot wound.

McCartney's "Got to Get You into My Life" was influenced by the Motown Sound[14] and used brass instrumentation extensively. Although cast in the form of a love song, McCartney described the song as an "ode to pot". It was released as a single in the US in 1976, ten years after Revolver, to promote the compilation album Rock 'n' Roll Music on which it appeared. (The vocal in the fade out at the end of the song is different on the mono version than on the stereo version. The last text line "What are you doing to my life?" can only be heard on the mono version).

McCartney also contributed "Here, There and Everywhere", "Good Day Sunshine", "Yellow Submarine" and "For No One", a melancholy song featuring him playing clavichord and a horn solo played by Alan Civil. He also played the guitar solo on "Taxman".

Revolver was also a breakthrough album for Harrison as a songwriter, and he contributed three songs on the album, including the opening track, "Taxman". The song was a protest against the high marginal rates of income tax paid by high earners like the Beatles, which were sometimes as much as 95 percent of their income (hence the lyric, "There's one for you, nineteen for me"). The "Mr Wilson" and "Mr Heath" referred to in the lyrics are Harold Wilson and Edward Heath, who were, respectively, the British Labour Prime Minister and Conservative Leader of the Opposition at the time. In the Anthology 2 version, the "Mr Wilson" and "Mr Heath" backing vocals were replaced with "Anybody got a little money".

Harrison also wrote "I Want to Tell You", about his difficulty expressing himself in words. "Love You To" marked a significant expansion of his burgeoning interest in Indian music and the sitar, which started with "Norwegian Wood (This Bird Has Flown)" on Rubber Soul. It was the intro to "Love You To" that was playing in the background when Harrison's character first appears in Yellow Submarine, the animated Beatles film released in 1968.

Ringo Starr's only lead vocal on Revolver is the childlike "Yellow Submarine". McCartney said that he wrote "Yellow Submarine" as a children's song for Starr to sing. With the help of their EMI production team, The Beatles overdubbed stock sound effects they found in the Abbey Road Studios tape library.

According to music critic Richie Unterberger of Allmusic:

In many respects, Revolver is one of the very first psychedelic LPs – not only in its numerous shifts in mood and production texture, but in its innovative manipulation of amplification and electronics to produce new sounds on guitars and other instruments. Specific, widely-heralded examples include the backwards riffs of "I'm Only Sleeping", the sound effects of "Yellow Submarine", the sitar of "Love You To", the blurry guitars of "She Said, She Said", and above all the seagull chanting, buzzing drones, megaphone vocals, free-association philosophizing, and varispeed tape effects of "Tomorrow Never Knows".

In 1972, Lennon offered some context for the influence of drugs on The Beatles' creativity:

It's like saying, "Did Dylan Thomas write Under Milk Wood on beer?" What does that have to do with it? The beer is to prevent the rest of the world from crowding in on you. The drugs are to prevent the rest of the world from crowding in on you. They don't make you write any better. I never wrote any better stuff because I was on acid or not on acid.

—John Lennon, The Beatles Anthology

According to music critic Jim DeRogatis:

Revolver, Pet Sounds and The Piper at the Gates of Dawn, relics of the first era of psychedelic rock and shining testaments to what can be accomplished in the recording studio when folks are fuelled on the potent drug of rampant imagination.

—J. DeRogatis, Milk it!: collected musings on the alternative music explosion of the 90s

The cover illustration was created by German-born bassist and artist Klaus Voormann, one of the Beatles' oldest friends from their days at the Star Club in Hamburg. Voormann's illustration, part line drawing and part collage, included photographs by Robert Whitaker, who also took the back cover photographs and many other images of the group between 1964 and 1966, such as the infamous "butcher cover" for Yesterday and Today. Voormann's own photo as well as his name (Klaus O. W. Voormann) is worked into Harrison's hair on the right-hand side of the cover. In the Revolver cover appearing in his artwork for Anthology 3, he replaced this image with a more recent photo. Harrison's Revolver image was seen again on his single release of "When We Was Fab" along with an updated version of the same image.

The title "Revolver", like "Rubber Soul" before it, is a pun, referring both to a kind of handgun as well as the "revolving" motion of the record as it is played on a turntable. The Beatles had a difficult time coming up with this title. According to Barry Miles in his book Paul McCartney: Many Years from Now, the title that the four had originally wanted was Abracadabra, until they discovered that another band had already used it. After that, opinion split: Lennon wanted to call it Four Sides of the Eternal Triangle and Starr jokingly suggested After Geography, playing on The Rolling Stones' recently released Aftermath LP. Other suggestions included Magical Circles, Beatles on Safari, Pendulum, and, finally, Revolver, whose wordplay was the one that all four agreed upon. The title was chosen while the band were on tour in Japan in June–July 1966. Due to security measures, they spent much of their time in their Tokyo Hilton hotel room; the name Revolver was selected as all four collaborated on a large psychedelic painting.