Physicists have broken the record for the most accurate clock

There's a team working at JILA in colorado who've achieved something similar with Strontium: http://arxiv.org/abs/1412.8261

Edit: One of the reasons to build these clocks is to find out if the fundamental constants really are unchanging. So they build two clocks that rely on different relations of fundamental constants, and see if the "ticking" of the clocks changes with respect to each other. See: http://arxiv.org/pdf/1407.4408.pdf for info on that.