The DF-31 has been in development for over twenty years and only had its first successful launch twelve years ago. It's now believed to have a reliable and accurate guidance system, as well as a third stage that carries multiple 50 kiloton nuclear warheads. Only about a dozen DF-31s are in service, plus about a dozen DF-31As. Many of these appear to be aimed at European Russia.
Last July the new DF-41 ICBM with multiple warheads was tested. China can apparently put 3-10 warheads in the DF-41 final stage. The DF-41 has not been displayed publicly but thanks to most Chinese having cell phones, and many knowing how to send photos to foreign web sites without getting arrested, there are photos of the DF-41 available. The DF-41 appears to have had a lot of development problems because few have been built and fewer (less than a dozen) put into service. The DF-41 is the only Chinese ICBM that can reach all of the United States.
Three years ago China announced that its nuclear armed ballistic missiles were not aimed at anyone. Like most countries, China has long refused to say who its nuclear armed missiles are aimed at. Most of those missiles only have enough range to hit Russia or India, or other nearby nations. For a long time most were very definitely aimed at Russia, which had rocky relations with China from the 1960s to the 1990s. But after the Soviet Union dissolved in 1991, the new and much smaller Russia became friendlier with the wealthier (more capitalist but still run by communists) China. Relations between China and India also warmed up and then went into a deep freeze during the past decade.
China is believed to have over 400 nuclear warheads, most of them installed on ballistic missiles. Only a few dozen of these missiles can reach the United States. These include the older (and about to be retired) DF-5, plus the newer DF-31A and DF-41. For the last two decades China has had about two dozen DF-5 ICBMs, their only missiles that can reach the United States. Few of these are believed to be operational because of reliability and maintenance problems. The U.S. has since installed 18 ICBM interceptor missile systems in Alaska. These are to deal with North Korean missiles but could also destroy most Chinese missiles headed for the United States. Thus it makes sense for China to simply say that it is not aiming any of its missiles at anyone. Modern guidance systems can be quickly (in less than an hour) programmed for a new target, so it doesn't really matter that, normally, the missiles have no target information in them. The DF-5s, moreover, are liquid fueled and the considerable activity required to ready them for launch can be detected by spy satellites.
The DF-5s are to be replaced by solid fuel DF-41s. These missiles can be moved, erected, and launched from a special truck. With a 15,000 kilometer range they can reach all of the United States. The third stage contains 3-10 warheads, each with an explosive yield of at least 100 KT. The DF-41s appear similar to the American 36 ton Minuteman III (a 1960s design that has been much upgraded since then).
India is of growing concern to China but there are shorter range ballistic missiles, like the DF-21, to deal with that threat. The Chinese introduced the DF-21 in 1999, and now has over a hundred in service. Many have non-nuclear warheads. This missile has a range of over 1,800 kilometers and can haul a 300 kiloton nuclear warhead. It's a two stage, 15 ton, solid fuel rocket. Launched from Tibet, the DF-21 can reach most major targets in India.
Then there is a submarine launched missile the JL (Julang) 2 SLBM (Sea Launched Ballistic Missile). This missile has had a lot of problems as have the SSBNs (ballistic missile carrying nuclear subs) that carried them. The 42 ton JL-2 has a range of 8,000 kilometers and would enable China to aim missiles at any target in the United States from a 094 class SSBN cruising off Hawaii or Alaska. Each 094 boat can carry twelve of these missiles, which are naval versions of the existing land based 42 ton DF-31 ICBM. The JL-2 was supposed to have entered service three years ago but kept failing test launches. No Chinese SSBN has ever gone on a combat cruise because these boats have been very unreliable.
About two thirds of Chinese nuclear warheads are believed to be in missile warheads, most of them DF-21s. Normally, these warheads are stored separately and mated to the missiles only for actual use or the occasional training exercise.