North Korea claims to have tested a thermonuclear weapon (widely called a hydrogen or H-bomb). An excellent article Science News article (Thomas Sumner, "Five things science can (and can’t) tell us about North Korea’s nuclear test," January 6, 2016) summarizes the reasons why it is likely that North Korea detonated a nuclear weapon but not a thermonuclear device. Most basic, a thermonuclear weapon would have caused a much larger tremor.
On the one hand, North Korea's continuing nuclear weapons program does not cause any new worries. No other country is in a position to stop North Korea's weapons programs. Although the test has cause perturbations in China, North Korea's staunchest ally, China lacks the influence to persuade North Korea to change. China, like the US and other states, has more to lose than gain from waging a war to coerce North Korea to change.
North Korea's leadership clearly has some different values and goals than do the leaders of most states. However, North Korea's leadership has given no indication that it is either suicidal or intent or initiating a nuclear war that would result in total devastation of North Korea. The leaders of other states (e.g., President Obama) recognize North Korea's bluster, braggadocio, and attempts at bullying for what they are and wisely want to avoid the types of misinterpretations that erroneously led to the second Gulf War against Iraq.
On the other hand, the almost unfathomable destructive capacity of nuclear weapons (a small thermonuclear device packs a punch equivalent to 1,000 of the bombs the US dropped above Nagasaki in WWII) should prioritize arms control and non-proliferation.
First, the US should dramatically reduce its nuclear arsenal. These weapons and their delivery systems are expensive, needlessly redundant, and taunt other states to engage in unproductive arms races. One step the US could take unilaterally to deescalate nuclear weapons' competition is to eliminate the ground and air components of its nuclear triad, relying only upon ballistic missile submarines. These subs are virtually undetectable and pack sufficient punch to destroy any enemy five or more times (the number depends upon the enemy's size). Another step the US could take is to phase out ballistic missile subs as those subs reach the end of their expected service life (this will happen in the next decade). Instead of replacing the current Ohio class subs with a newer, yet more expensive ballistic missile sub, the US could modify some of its hunter-killer subs to launch ballistic missiles (these subs can already launch cruise missiles). The cost of the modifications, along with the cost of the missiles, will be less than a tenth the cost of replacing the Ohio class subs with a new class of ballistic missile subs. In a list of probable national security threats, nuclear war rates as highly unlikely. In an era of multiple real threats and limited defense dollars, the US and its citizens stand to gain much from eliminating wasteful, unnecessary programs and expenses.
Second, making these moves will earn the US significant credibility in the global community, thereby bolstering its efforts at both arms control and promoting nuclear non-proliferation. This will further enhance US national security interests at no cost to taxpayers.