In 1982, he finished runner-up in the European Junior Chess Championship. Two years later, Greenfeld won the Israeli national championship. His best individual achievement is the victory of the Komerční banka Cup, a category 14 round-robin tournament at the Trimex Open 1993 in Pardubice.
His most famous pupil has been Emil Sutovsky. He travels regularly to India, and works with a number of promising young Indian players e.g. Vidit. Asked what his best game was Greenfeld unhesitatingly replied: "My game against G.M. Boyce at Jersey 2004" 
Alon Greenfeld played for Israel in five Chess Olympiads.
- In 1982, at first reserve board in the 25th Chess Olympiad in Lucerne (+3 −1 =3);
- In 1984, at second board in the 26th Chess Olympiad in Thessaloniki (+6 −1 =6);
- In 1988, at first board in the 28th Chess Olympiad in Thessaloniki (+4 −5 =4);
- In 1990, at fourth board in the 29th Chess Olympiad in Novi Sad (+5 −2 =4);
- In 1994, at fourth board in the 31st Chess Olympiad in Moscow (+4 −2 =3).
Greenfeld was awarded the titles of International Master (IM) in 1983 and Grandmaster (GM) in 1989.
- Alon Greenfeld FIDE rating history, 1980-2001 at Olimpbase.org
- "C.to Europeo U20". LOTO - Lost Tournaments. Italian Chess Federation. Retrieved 2016-07-29.
- Alon Greenfeld at Chessmetrics
- "Year 1993". Czech Open. Retrieved 2016-07-29.
- Referring to untitled player G. Michael Boyce [http://www.chessgames.com/perl/chessgame?gid=1620619 Alon Greenfeld vs G Michael Boyce, Jersey open, r2, 2004; Queen's Indian Defense]
- Bartelski, Wojciech. "Men's Chess Olympiads: Alon Greenfeld". OlimpBase. Retrieved 2009-06-28.
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