* How would the US respond? * How would countries like China and Russia respond in turn? * Would it be the beginning of World War III?
The linked article is what prompted these questions.
Nuclear? Complete destruction of North Korea, which is why they'll never do it. Sadly Mutually Assured Destruction is the best deterrent to the use of nuclear weapons. This is also why terrorist organizations scare countries so much, it is hard to reciprocate when there isn't a clear actor.
What would be detected is a ballistic missile launch; while there's no "law" that every ballistic missile is nuclear, it is certainly the rule and there is no way to determine what kind of warhead an ICBM/SLBM carries in-flight. As soon as the launch is detected, countermeasures are imitated. The launch/boost time window is ~ 5 minutes long and without prior warning the U.S. would have to hope that by chance there's missile destroyer nearby, in order to try to intercept it. During midcourse the missile is almost undetectable, because it doesn't have an exhaust. So once the last booster falls off, the first window for interception closes.
Once the warhead reenters the atmosphere the second, shorter (approx. 2 minutes), time window would open. Terminal interception is very difficult because the warhead enters at terminal velocity with ~ 14000km/h (~8700mph). If the warhead would split up into several reentry warheads (socalled "MIRVs), a proper interception is almost impossible, even for the U.S. (but afaik the North Koreans are far from having that technology). Here are two videos from the old and discontinued Nike-Sprint interceptor missile, just to give an impression of how damned fast these things are (and the Sprint goes "only" 12000km/h!). In the second video you can see how the missile turns from black to white due to the enormous friction.
Europe is already a tinderbox, so let's hope no one tries to spark WWIII. They said WWI couldn't happen, and well, we all know how that turned out.
US has recently began mobilizing the majority of its navy into the pacific.As of right now it is the area with the most dangerous potential for things to go wrong. China has become increasingly aggressive to Japan with their island disputes and North Korea seems set to cause trouble in any way possible. I see it as a matter of time before some action is taken to prevent a tragedy in the future. China may be one of the only reasons actions have not been taken, they have extreme animosity the US and Japan and I feel if we were to step in and try to stabilize the region it would only end up in a total war with China. As of right now we will just have to wait it out, but you had better believe the US is getting ready for business.
I think that it will lead to a swift end to North Korea as we know it. Even if the US doesn't nuke NK they would probably take out their leadership within 24 hours of the attack. In addition to that, I think the US missile defence system could stop the missile before it reached the mainland. I don't think that either China or Russia care enough about NK for them to go to war over it. They even agreed with the 2006 and 2009 UN resolutions.
I think its going to be the continuation of Korean war, the second that the missile is determined to land in American territory, South Korea, or Japan, salvos will be launched by either three of those countries, which will lead to a quick peace treaty. I think a country like China, if they would publicly ally themselves with N. Korea, wouldn't put troops on the ground but would supply N. Korea with weapons, etc. while facing heavy sanctions from the EU. Russia wont ally themselves with N. Korea, but they will sell guns to them without any NATO trouble. I wouldn't say unit would be world war III in terms of battles, but either a proxy war (if the US isn't directly hit) or a continuation of the Korean war in which the US throws its full military support behind.