For those who haven't been following this story, dark matter likely makes up around 23% of all matter in the universe. But scientists thus far have not been able to observe it directly, because it interacts so weakly with ordinary matter; we only infer its existence from detecting their gravitational fields.
A physicist named Fritz Zwicky first noticed this phenomenon in 1933 when he concluded that galaxies in the Coma cluster were moving so quickly that they should be able to escape from the cluster if visible mass was the only thing contributing to the cluster's gravitational pull. Since the cluster hadn't flown apart, he proposed the existence of "dark matter" to account for the observational data.
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. What are they looking for? Well, they're not 100 percent sure, frankly, but they have some ideas. The leading candidate for dark matter is a Weakly Interacting Massive Particle (WIMP). But they also need to know where to look, in terms of range of mass. The more you can narrow the target range, the better your chances of detecting a WIMP. Most theorists seem to favor a "heavy WIMP" model - predicting a particle with a mass of around 100 GeV - while a few others have staked out a claim in favor of light WIMPs, with a mass of 7 or 8 GeV.
Each camp can cite hints of experimental evidence in its favor, but the issue is far from resolved. (Bear with me here, there are a lot of acronyms.) On the "light" side of the debate, you've got results from the Fermi Gamma-ray Space Telescope and DAMA, in which sodium iodide detectors are buried deep underground in the Gran Sasso mountains, emitting flashes of light (Cerenkov radiation) at those rare moments when dark matter particles collide with the detector material.
The strategy with DAMA is not to try to pick out individual dark matter signals from all that background noise, but instead to have tons of candidate events and look for slight changes in the number of observed events as the Earth orbits around the sun.
As Carroll explains, "Dark matter is like an atmosphere through which we are moving; when we're moving into a headwind, the rate of interactions should be slightly higher than when our relative speed through the ambient dark matter is smaller." The problem is that other experiments, employing complementary strategies, can't replicate DAMA's findings, making it more likely that the observed fluctuation isn't due to dark matter.
On the "heavy" side of the debate, you have the CDMS and XENON100 collaborations. XENON100 uses 100 kg of liquid xenon deep underground in the same Gran Sasso mountains. Xenon is a very heavy element, and thus has a larger cross section, which determines the number of likely collisions (larger is better). XENON scientists say their results - or lack thereof, since they don't see evidence for "light" WIMPs - rule out the light WIMP scenario.