Usually these are
The first two are useful because the large amount of energy given out damages people and infrastructure. All of them have the property they they are highly pollutive.
Fission based weapons have been around since the USA dropped two on Japan at the end of the second world war. Making them small is difficult, but the technology is pretty simple. The cost to make one has been estimated at $AU1M-$AU2M, plus the cost of the bomb-grade Uranium235.
Fusion weapons are more advanced (they use a fission reaction to start them), and require a significant infrastructure for even a major country.
Dirty weapons are just conventional explosives mixed with radioactive material which spread the material around. They are effectively zero cost once the radioactive material has been obtained.
All of these weapons leave radioactive material around for a very long time, and the radioactive material harms humans. A bomb can make an area unsuitable for human habitation for many human life-times. A major nuclear war would make much of the earth (and some believe all of the earth) unsuitable for human habitation for the foreseeable future.
This is the reason that they have a bad reputation. Killing people is one thing, but damaging infrastructure is considered by many to be too high a price for just winning a war.
Stable countries with nuclear weapons increases world stability. No rational government would invade a nuclear-armed country because their people and their infrastructure will be destroyed in the process - the behavior is irrational both from an collective and individual viewpoint.
Unfortunately the same is not true of religious zealots. A religious zealot with the bomb is likely to decide that their god wants to create Armageddon on earth, and nuke as many infidels as possible. Historically death and human suffering are not things which religions bother avoiding.
Ironically nuclear profileration is most opposed by left-wing groups, who are opposed to infrastructure, and the exploitation of the earth. A major nuclear war would actually be a really good thing for the earth's ecology.
Radioactivity will effect all living things to some extent, but the major effects are on large animals, which live a long time, and which have a low fertility rate. Think this through - a death rate of 90% is catastrophic for humans (you couldn't realistically achieve a positive population growth without very high technology), but would hardly even affect cockroaches. When they lay thousands, and sometimes millions of eggs in their lives only two (on average) survive being eaten, or starved because of competition from other cockroaches. Laying 90% defective eggs will make little difference to them.
Basically radiation is harmful to humans, and a few other mammal species. These could die out, but the rest of the world's animal population would be rather unaffected. Quite the ecologist's dream.
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