Third World Love began as a booking, not a band. Four musicians who knew each other from New York were put together in Barcelona in July 2002 for a single tour: trumpeter Avishai Cohen, pianist Yonathan Avishai, bassist Omer Avital and drummer Daniel Freedman. The first tune they played together was Wayne Shorter's "Juju," and by the label's own account the group knew within thirty seconds that the one-off was going to become something permanent. Three of the four were Israeli-born; Freedman was a New Yorker who had come up in the 1990s at Smalls Jazz Club, in the same Greenwich Village circle as Avital, and had played in Avital's sextet there. Avishai was already living in France, and Cohen and Avital were based in New York.

The tour produced a record almost immediately. Third World Love Songs was cut at Estudi Moraleda in Barcelona on July 8 and 9, 2002, with Jordi Pujol, the owner of Fresh Sound Records, as executive producer, and came out that year on the label's Fresh Sound World Jazz imprint (FSWJ 023). All four members are credited as producers, and Freedman shares the mixing credit with engineer Jordi Vidal. It is six long pieces across 59 minutes, three of them past eleven, with Avishai doubling on flute. Two titles fix the circumstances of the session: the closing miniature "Sketch of Barcelona," and "Musicians Without Boundaries," Avishai's tune dedicated to Arnie Lawrence, the American alto saxophonist who co-founded the New School's jazz program in 1986 and moved to Jerusalem in 1997 to run the International Center for Creative Music there.

The band's second phase was an Israeli one. NMC Music, the Tel Aviv label, put out a promotional maxi-single, Africa Mousso (CDDJ 2035), in 2003, pairing a remix of "La Suite Africain" with the album version and an enhanced video track. The album followed on September 27, 2004: Avanim (NMC 330263-2), Hebrew for "stones," recorded at Zaza Studios in Tel Aviv. It is the most openly non-jazz record in the catalog, with Avital adding oud and electric bass, Avishai on electric piano and all four singing. NMC put three of its tracks on a promotional sampler for the Womex world-music trade fair that same year, which is a fair indication of how the label was positioning the group. The band's live following in Israel grew accordingly: press accounts describe crowds of a thousand or more treating the concerts as dance events rather than jazz recitals.

Sketch of Tel Aviv, recorded July 24 and 25, 2005 at Haogen Studios in Israel and released October 10, 2006, moved the band onto an American label, Smalls Records (SRCD-0018), the imprint attached to the Village club where Avital and Freedman had built their reputations. Uri Barak engineered, Michael Perez-Cisneros mastered, and Anna Prats did the artwork. Cohen wrote four of the eight pieces, Avital two, Avishai the title track, with the Yemenite Jewish traditional "Hareshut" opened by Avital on unaccompanied oud. Israeli singer-songwriter Eviatar Banai guests on vocals on "Horizon (Kav Ha'ofek)." Reviewers in the United States picked up on the range: JazzTimes called it bold and infectious, PopMatters gave it 6 out of 10 while noting that the quartet was flirting with a very large number of idioms at once.

For the last two albums the band moved again, to Anzic Records, the label Anat Cohen co-founded and the trumpeter's own home label at the time. New Blues was recorded March 16 and 17, 2007 at Avatar Studios in New York, recorded and mixed by Joe Ferla, produced by the band, and released March 4, 2008 (ANZ 7301). Eleven tracks, ten of them originals by Cohen, Avital, Avishai and Freedman, closing with Duke Ellington's rarely covered "So." Scott Yanow, reviewing it for AllMusic, described the group plainly as an advanced jazz quartet whose Israeli ties shaped its compositions rather than a world-music project. Songs and Portraits, the fifth and last album, was taped at Flux Studios in New York in April 2009 with Fab Dupont engineering, then sat for years: Perez-Cisneros and Freedman mixed it, Gene Paul and Jamie Polaski mastered it, and pianist Daniel Sarid wrote the liner note. Anzic catalogued the CD as 2011 (ANZ-7302), Bandcamp dates the digital release February 1, 2012, and the label's own publicity campaign ran in April 2012, with release concerts at 92Y Tribeca in New York on April 26 (a double bill with Jason Lindner's Now Vs. Now) and at the SFJazz Spring Season's Israeli Jazz Fest in San Francisco on April 28. It opens with an arrangement of the Yemenite liturgical "Im Ninalu" and contains Freedman's "Alona," a ballad written for his six-month-old daughter, and Avital's three-part Sephardic sequence "Sefarad," "The Abutbuls" and "The Immigrant's Anthem." JazzTimes, reviewing it in August 2012, called it one of the jazziest albums either Avital or Cohen had made.

The group has never announced a breakup, and it has not recorded since. By its own account it went nearly four years without playing at all in the late 2000s, reconvened in 2011 and toured Israel in January 2012, opening at the Zappa Club in Tel Aviv and closing on January 21 at the Red Sea Winter Jazz Festival in Eilat. Then it went quiet for a decade. On November 10, 2022 the four reconvened once more, opening the Red Sea Jazz Festival at the Port Arena in Eilat under the billing "The Reunion," with Amir Bresler in the drum chair rather than Freedman, the only lineup change in the band's history. DownBeat, previewing it, described a group returning after nearly a decade off the stage for a single show booked exclusively for that festival. Nothing has been documented since.

The band's identity was never a concept, and all four members have said so: Avital's summary is that the friendship and the closeness among them are what did it, and Cohen's is that Avishai brought lyricism and balance, Freedman the New York touch, Avital the vibes and Cohen the rock and roll. What that produced on record is a quartet that treats North African, Yemenite, Sephardic, flamenco and Ethiopian material as repertoire rather than as decoration, over a rhythm section that swings when it wants to and plays straight-out grooves when it does not. Every member composed for every album, which is unusual for a band with two figures as strong as Cohen and Avital in it, and is the main reason the records feel collective rather than led. The trajectory runs backwards from what the name suggests: the early records lean hardest on world-music elements, with singing, oud and remix singles, and the later ones move toward jazz. Critics tracked that shift. All About Jazz's Mark F. Turner heard American ragtime inside the title track of Sketch of Tel Aviv; Greg Camphire, reviewing New Blues for the same site, listed swing, Dixieland, post-bop, flamenco, salsa, samba and klezmer as reference points on a single record; JazzTimes concluded that Songs and Portraits was the jazziest thing its two principals had done. AllMusic files the band under Contemporary Jazz, Neo-Bop and Progressive Jazz.