Until you delve pretty deeply into the nature of the containment problem for controlled fusion, it's all but impossible to comprehend just how huge a problem it really is. oldprof's analogy of a universal solvent is well-chosen, and it informs you how impossible it is, using ordinary matter as a vessel. So what has been done, going back to the 1960's and before, is to try to use strong magnetic fields to contain the hot plasma.
About the time oldprof reports having worked where research on this was being done, I was in grad school in physics. At my university, there was one such project -- a magnetic mirror machine. In this concept, magnetic fields are set up to cause the charged particles, while spiraling around the magnetic field lines, to bounce back and forth between the opposite ends of the device, where the fields are stronger, which makes the particles "reflect" at each end. Problem is, there is some inevitable leakage at each reflection, and because the reflections happen so rapidly, the plasma dissipates before anything useful can be done.
In the early 60's, the Soviets and the Americans each had a toroidal (doughnut-shaped) device to confine the plasma; the former called, Tokamak, the latter known as, Stellerator. Both designs were tweaked for many years, each one by both 'camps,' without eventual success. The problem is basically like trying to wield a million forks quickly and accurately enough to prevent millions of strands of spaghetti from escaping at high velocity.
Another idea was laser fusion, aka, inertial confinement, in which pellets of deuterium-tritium fuel are blasted with high-powered laser pulses to compress and heat them enough to initiate nuclear ignition. This is somewhat like squeezing a ball of clay very hard, simultaneously and uniformly enough from all possible directions to prevent any of it from squirting out due to even the slightest nonuniformities in the applied pressure.
Basically, there have been decades of theoretical and experimental research on this problem, at the cost of a king's ransom, and we're still very far from even knowing how controlled fusion can be achieved, or whether it even can be. So it's not like there hasn't already been an effort of Manhattan-Project magnitude on this, and it's difficult to see what more could be done, without committing far too much money and manpower to justify an uncertain result. What is needed to change that, is a truly novel idea, backed up by some unexpected experimental success. Failing that, the research should continue at reasonable, not Herculean levels of effort.
So far, the only method of containment known to be successful is gravitational containment, and all you need to construct such a fusion reactor, is about a solar mass of hydrogen.
It's called a star.