She obtained a master's degree from the University of Canterbury with her thesis being titled Re/producing the nation : women making identity in New Zealand, 1906–1925.

[1][5] She succeeded Jim Anderton, who had announced that he would retire either after winning the Christchurch mayoralty (he was unsuccessful) or at the end of the term of the 49th Parliament in November 2011.

[11] Anderton remained an MP until the end of the term of the 49th Parliament, and Woods won in the 2011 general election in the Wigram electorate.

On 12 April, Woods announced that the Government would halt future gas and oil exploration but clarified that the existing 22 contracts would be allowed to continue.

[23] In early November 2020, she retained her ministerial portfolios of Housing, Energy and Resources, and Research, Science and Innovation, while picking up the position of Associate Minister of Finance.

[24] In late February 2021, Woods defended the Government's Progressive Home Ownership Scheme, which had cost NZ$17 million but only resettled 12 families in the last seven months.

[22] In early June 2023, she attracted media attention after publishing a Twitter post likening the opposition National Party's proposal to bring back the NZ$5 prescription fee to the dsytopian novel and TV show The Handmaid's Tale.

In response, National's deputy leader Willis stated she was offended by Woods' post and accused the Labour Government of "going into the gutter" and making "ridicolous, baseless attacks.

[28] In late November 2023, Woods became spokesperson for climate change, energy, resources and associate finance in the Shadow Cabinet of Chris Hipkins.