A key observational tool in cosmology is the measurement of the expansion history of the Universe that is possible with spectroscopic galaxy redshift surveys. Until now, the best constraints on this have come from a combination of BAO and redshift-space distortions (RSD), which allow measurements of the angular diameter distance D_A, the Hubble rate H, and the growth rate as a function of redshift. I will describe a new technique to measure these quantities from the same data by using the anisotropic distribution of galaxies around cosmic voids. Applying this method to data from the SDSS BOSS galaxy survey provides a 1% measurement of the Alcock-Paczynski parameter D_A*H/c at z=0.57, which is better than the BAO constraint by a factor of almost 4. Combining void results with BAO and RSD constraints leads to an increase in precision of around 40-50% on each of D_A, H and the growth rate, equivalent to a huge increase in the survey data volume using traditional methods alone! I will discuss the implications for dark energy measurements, and applications to future surveys.