North Korea has carried out several nuclear tests and in fact has recently applied to be formally recognised as a nuclear power.
THe last test was carried out in February 2013, and recently some radioactive traces have been found near Japan, possibly as a result of this test. It is now rumoured that they may be about to carry out a fourth test, possibly of a missile that could reach as far as Guam; however, similar claims were made about the February test and they haven't yet been proved.
As far as is known from outside, the republic does have several nuclear facilities, some of which are unknown to observers, and it does have enough weapons grade plutonium to produce some bombs. However, it doesn't seem to have managed to create a viable warhead yet, and also does not appear to be using uranium, which would suggest a much more advanced capability.
So at present it would seem that North Korea has weapons, but isn't yet in a position to deploy them - however, we don't know how long this will be the case. You can learn more here.