Greenberg had early success when in 1990, at the age of fifteen, she published The Digits, a series of twelve books featuring her fingerprints as characters. She has written and illustrated a number of other children's books, including Squids Suck (2005),Antonia Cutlass Walks the Plank (2006), and Operation Weasel Ball (2007). Greenberg is a regular contributor to the regular Australian comics anthology Tango, edited by Bernard Caleo and published by Cardigan Comics.
In 2009, Greenberg's work appeared in Super Heroes and Schlemiels: Jews and Comic Art, an exhibition of comic art at the Jewish Museum of Australia in Melbourne. She has been interviewed by The New Yorker in its on-line cartoon forum, by Jennifer Byrne on ABC1 television and The Book Show on ABC radio.