So I just went and looked this up and,
Fusion reactors do, in fact, exist, and you can even build a Farnsworth reactor yourself. What they haven't achieved yet is a self-sustaining reaction that produces more power than it takes to keep the reaction going. They're hoping to achieve this with ITER, and there's a group in the UK trying to achieve commercial fusion power by 2040, but I'll believe that when I see it. The device featured in STID is the test chamber at the National Ignition Facility.
edit: and I've been beaten to it