I'm resurrecting this thread since North-Korea seems hellbent on causing the first nuclear war.
To freshen up the common knowledge base, North-Korea has both missiles and nukes. What is currently unknown is whether they have successfully miniaturised nuclear warheads sufficiently so that they can be fitted into a ballistic missile.
First, the nukes. Demoractic People's Republic of Korea - which is neither democratic nor a republic - has done several nuclear tests. Back in 2006 they tested a decide with a yield of 0.2 - 1 kilotons. In 2009 they did the second test, with a yield of 2 - 7 kilotons. Third test was done in 2013 and its yield was 7 - 8 kilotons. In 2006, DPRK had two nuclear tests and claimed that they had tested a hydrogen bomb - a far more destructive device than an atomic bomb - but experts were suspicious of this claim. The second test allegedly proved that DPRK had mated a nuclear device with a ballistic missile but again, evidence is lacking.
The sixth test took place yesterday (3rd September 2017) and the yield was vastly higher, around 100 kilotons, though other estimates have placed it as low as 50 kilotons and as high as 200 kilotons. DPRK again claimed that it was a hydrogen bomb mated with a ballistic missile. The destructive power suggests that this time they might not be lying.
DPRK has multiple facilities for producing nuclear material and if left in peace, can start stockpiling bombs now that they have "proper" working nukes. Estimates on their current warhead stockpile range from 20 to 60.
Now, while even 1 kiloton bomb is quite devastating, it's not that much worse than conventional weaponry. But a 100 kiloton bomb is certainly a "real" nuke and can cause tremendous damage. I've used Alex Wellerstein's nukemap to give you some examples, using an air-bust model for a 100 kT blast:
Tokyo
Los Angeles
Seoul
USN base at Guam
USAF base at Guam
So you can see that a 100 kiloton air-burst, while terribly devastating, is not quite the individual world destroyer that the megaton class bombs are. Nevertheless, DPRK has several.
Then, the missiles. DPRK has hundreds and hundreds of missiles but the vast majority of them are short-ranged, either artillery missiles, cruise missiles or theatre ballistic missiles. Dangerous mostly to South-Korea and somewhat to Japan. For the rest of the world, the most dangerous missiles are Hwasong-12 and Hwasong-14. The former has a range of up to 6000 kilometres and the latter up to 10,000 kilometres. However, test results have been mixed. Many missiles have broken up on re-entry and there is no hard information on their accuracy. Remember that it took the United States and Soviet Union decades of work to get ICBM CEP under 10 kilometres, not to mention under 1 klick. Hwasong-14 is basically just Hwasong-12 with an added second stage and thus reduced payload capability.
So DRPK can probably only nuke South-Korea and Japan - possibly Taiwan/Okinawa/Guam (if they can hit it). Reaching Alaska or Hawaii is questionable, not to mention Thailand, Australia or US western seaboard.
What can be done?
United States is perfectly capable of destroying DPRK even without using their own nuclear arsenal. Unfortunately any military action against the North risks massive retaliation against the South, and the ROK capital of Seoul is reachable for even the shortest range DPRK missiles. DPRK also have chemical weapons that they can put on their short range missiles. Evacuating a city of nearly 10 million people is of course impossible.
Covert action is less profitable. DPRK is extremely secretive and successful penetration of their nuclear program is even more difficult than with Iran. The success of eliminating leading Iranian scientists has largely been thanks to Mossad. Whether the South-Korean intelligence agencies can copy that success is questionable and CIA certainly cannot. And without up-to-date, accurate intelligence, hitting the useful and important targets becomes impossible.
So, diplomatic action seems the only sane option available. But it seems that DPRK is willing to lose their only remaining friend, China, in order to become a fully fledged member of the nuclear club. China can do more, like expelling the North-Korean workers from the special economic zone on the border. But if freezing coal purchases from DPRK did not deter them, other soft-power actions are likely to be just as ineffectual.