Radiological warfare is any form of warfare involving deliberate radiation poisoning, without relying on nuclear fission or nuclear fusion.
Radiological weapons are normally considered weapons of mass destruction, and are very commonly equated with a radiological bomb often mis-called a "dirty bomb" (which refers to a nuclear weapon with a radiological side effect). However, bombs are very inefficient ways to spread radiation, and all such special weapons have problems that render them likely impractical for military uses.
Rather, radiological warfare would be of vastly more use to terrorists spreading or intensifying FUD. The release of radioactive material may involve no special "weapon" and include no direct killing of people, but rather make whole areas or structures unusable or doubtfully useful for the support of human life, due to the exposures of staying too near them for long periods. For instance, a city such as Washington DC could perhaps be rendered uninhabitable or at least quite undesirable - radiation being extraordinarily difficult to remove once it is released into the built environment, and perhaps taking a long time to fully decay in the natural environment. Like land mines, it can be an area-denial method.
A much more efficient way to kill huge numbers of people, as documented as the main point of the science fiction story Solution Unsatisfactory, published by Robert A. Heinlein in 1940, is to use conventional aircraft to "dust" large areas from above. This story predicts the precise power structure of the atomic age, based on mutual assured destruction and a permanent Mexican standoff, without postulating the atomic bomb (although such was the subject of Deadline, another such prophetic story by Cleve Cartmill, published in 1944).
Current concerns about radiological warfare tend to be focused on "bombs" but also on deliberate pollution of water supply. Some agents, such as plutonium, are extremely virulent, and can kill over time with near-certainty at doses as low as one microgram. However, being an extremely heavy metal, and extremely dangerous and difficult to grind to powder, it seems unlikely that it would be an effective means of such warfare. In Heinlein's story, Uranium 235 is used. However, this has more or less the same problems as Plutonium.
It is more likely that lighter elements might be used, those isotopes that are very unstable and may be created just in time for use. However, these require intensive industrial infrastructure and expertise to create and cannot be retained for long periods. It is therefore believed that the existing regimes of inspection of labs and other facilities handling radioactive material, if strictly enforced, can effectively prevent their use to kill in a systematic and deliberate manner. For these reasons, some experts consider radiological warfare to have the same problems as chemical warfare.
Caesium-137 is sometimes cited as a practical element for radiological warfare - it is widely used in nuclear medicine. However, for this very reason, it is subject to the dual regimes of medical and nuclear material controls, and is typically available only in such small quantities that any such use amounts to assassination or at most, mass murder, not effective warfare.
Should some technological change make radioactive materials more widely available, however, this form of warfare or at least terrorism might well become quite popular. In contrast to biological warfare, the results of radiological warfare are quite predictable, and the detection of radiation is quite easy and effective.
Should humans continue both technological escalation and wars between nation-states, radiological warfare might well be a far more safe and humane way to conduct extermination of large numbers of people, or the emptying out of troublesome political centres, than any of the various biological alternatives.