She began as a child actress on television, making her feature film debut in Because of Winn-Dixie (2005), followed by the supporting role of Violet Beauregarde in Tim Burton's Charlie and the Chocolate Factory (2005).

[11] After appearing in a commercial for McDonald's, Robb had a small role in "Number One Fan", an episode of the television series Drake & Josh.

The latter was a major box office success worldwide, and helped escalate Robb's popularity among preteen audiences.

Robb played Leslie Burke in Bridge to Terabithia with Josh Hutcherson, which opened in U.S. theaters on February 16, 2007.

She recorded a song for the soundtrack titled, "Keep Your Mind Wide Open", and the accompanying video received rotation on the Disney Channel.

[4][12] The song peaked at number 90 on the Billboard Hot 100 during the week of March 1, 2007, giving Robb her first charting single.

Time film critic Richard Schickel said: "There is a wonderful range to Robb's work...this is extraordinarily mature acting from someone this young and she wins our sympathy without once begging for it.

She then starred in Soul Surfer, playing Bethany Hamilton, who continued to surf after losing her arm in a shark attack.

[22][23] Robb played the role of Alice Green in the PBS Civil War historical drama series Mercy Street from 2016 to 2017.