In the 1960s, Vera Rubin and Kent Ford confirmed Zwicky's theory when their spectral analysis revealed that the outer stars in selected spiral galaxies were orbiting just as quickly as those at the center.
The visible matter wasn't sufficient to account for this; the spiral galaxy should be flying apart. Clearly, there had to be some kind of hidden "dark" mass adding to the galaxy's gravitational influence.
Physicists have been trying to directly observe dark matter ever since. We can, however, indirectly observe dark matter through gravitational lensing. That extra mass exerts a gravitational force on the space-time surrounding it. As light travels from distant galaxies, it will be bent around gravitational distortions in space-time - much like the paths of marbles rolling across a bent sheet of plastic - being caused by the dense regions of dark matter.
But gravitational lensing is a small effect, and difficult to detect for individual galaxies. That's why the SDSS data is so important: now scientists have images of millions of galaxies at their disposal. In 2010, an international research group used that data to determine the distribution of projected matter density from the center of galaxies out to a hundred million light years.