- Drafted by the Toronto Blue Jays in the 1st round (16th pick) of the 1991 amateur draft.
- Graduated from Tustin (California) High School.
- Donates $250,000 of his salary during each year of his contract to the Dodgers' Dream Foundation, totaling $1.5 million over six years. These contributions have supported the development of four Dodger Dream Fields throughout the City of Los Angeles and the purchase of books for local elementary schools and youth community programs as part of the Dodgers Reading Dugout Program.
- Made his Major League Baseball debut on September 28, 1993.
- Despite having his most productive years with the Los Angeles Dodgers, he was traded in late 2004 to the Arizona Diamondbacks.
- Was drafted by the Toronto Blue Jays (MLB) in the 1st round (16th pick) of the 1991 amateur draft.
- Has one daughter, Presley Taylor (born 22 December 2002).
- Second daughter, Chandler Rose (born 26 August 2005).
- Daughters, Presley Taylor & Chandler Rose
- Inducted into the National Jewish Sports Hall of Fame in 2005.
- Turned down a baseball scholarship to Stanford University.
- (January 9) Traded by the Los Angeles Dodgers to the Arizona Diamondbacks after waiving his no trade clause. The deal allowed the Diamondbacks to send Randy Johnson to the New York Yankees via the Dodgers in exchange for Green, pitchers Javier Vazquez, Brad Halsey and $19 million. (2005)
- Traded by the Los Angeles Dodgers to the Arizona Diamondbacks. (December 2004)
- Inducted into the International Jewish Sports Hall of Fame in 2014.
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