As for whether breakeven is even possible (not counting H-bombs), we have to get a little technical. 'Breakeven' is defined as when the input power is equal to output power. However to generate net power, the fusion output power needs to be converted to electricity and fed into the reactor, which means there will be thermodynamic losses. A typical ratio quoted for net power generation, also termed 'ignition', is 1:5. ITER is shooting for 1:10.
The current record holder is the JT-60 tokamak in Japan. It has achieved slightly better than breakeven, with a caveat: these are simulated numbers. You see, for safety and convenience, JT-60 does not use tritium, just deuterium, so the numbers are extrapolated from the D-D case to the D-T case. This does not strike me as a major issue since other tokamaks (JET) have run with tritium, but I am not an expert.
Tokamaks are the furthest along in terms of achieving ignition, but there are still a host of practical issues that need to be solved before the technology can be commercialized.
http://en.wikipedia.org/wiki/JT-60 http://en.wikipedia.org/wiki/Lawson_criterion
http://en.wikipedia.org/wiki/Fusor
The catch is doing it in a way that actually produces a surplus of energy that isn't a bomb. NB Even with bombs, most H-bomb designs actually get more energy from fission than fusion.
Edit: I wish there was some rule that said that a small percentage of mega-projects like ITER had to be used to fund competing approaches like this.