Recent experiments involve slowing down the speed of light to very much below its value in vacuum (c). How is this possible?

Here's a link to a news article on one such experiment.

Although the speed of light in a vacuum is constant, light slows down when travelling through a medium. This doesn't make much difference when it is travelling through air, but it does make a difference in many other media. For example, light going through glass slows down to two-thirds its speed in a vacuum. Just like it's harder for a person to move through water than through air (so people swim slower than they run), photons (massless particles that make up light) move slower when going through a medium that is difficult for them. Certain states of matter slow light down a huge amount (imagine a person trying to run through a tank of molasses or silly putty), and by using these states of matter, scientists can slow light down to a "human" speed. I'm not an expert on the physics involved, so here's a link that will provide you with more information.