In 1982, he was European Junior Sub-Champion.
More recently, Alon has concentrated in the fields of chess coaching. His most famous pupil has been Emil Sutovsky (who is now  working as a second for Gata Kamsky). 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 GM 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).
His best individual achievement was a victory at Pardubice 1993.
Greenfeld was awarded the International Master (IM) title in 1983, and the GM title in 1989.
- Bartelski, Wojciech. "Men's Chess Olympiads: Alon Greenfeld". OlimpBase. Retrieved 2009-06-28.
- Sonas, Jeff. "Chessmetrics Player Profile: Alon Greenfeld". ChessMetrics.com. Retrieved 2009-06-28.
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