The accelerating expansion of the universe, attributed to dark energy , has no accepted theoretical explanation. The origin of this phenomenon unambiguously implicates new physics via a novel form of matter exerting negative pressure or an alteration to Einstein s general relativity. These profound consequences have inspired a new generation of cosmological surveys that will measure the influence of dark energy using various techniques. One of the forerunners is the WiggleZ Survey at the Anglo-Australian Telescope, a new large-scale high-redshift galaxy survey that is now 50 complete and scheduled to finish in 2010. The WiggleZ project is aiming to map the cosmic expansion history using delicate features in the galaxy clustering pattern imprinted 13.7 billion years ago. In this article we outline the survey design and context, and predict the science highlights. A? 2008 Royal Astronomical Society.