Here we are mostly concerned with gamma rays, alpha and beta particles and neutrons since, besides being emitted in the form of radiation in the radioactive decay process, all four of them are generated in a nuclear explosion. When the nucleus of an atom contains a diverse number of electrons as compared to the stable configuration of the atom it disintegrates, emitting, in the process, subatomic particles and photons. When a photon collides with a stable atom some of the atom's electrons may be expelled; these electrons may subsequently bond to another atom giving it a negative electrical charge. The greater part of the initial radiation, or ionizing radiation, and emitted within the first minute from the detonation, is due to innumerable billions of electrons freed in the fission process from the rapid chain reaction which will thence emit: ultraviolet rays which are part of the fireball created by the explosion; X rays which contribute to the process of heat propagation; thermal radiation; gamma and, in a lesser measure, alpha and beta radiation. Radiations due to the excited state of neutrons are particularly penetrating, as well as gamma rays which can penetrate several hundred meters in the air, tens of meters in the water or in the soil and for several meters in materials of higher density, for example, metals.
When this radiations pass through biological organisms they cause direct damages to the tissues or interfere with the processes of cellular reproduction thus impairing the normal physiological function affecting part or all of an organism. This irradiation may result in radiation syndrome: low doses cause diarrhea and nausea and vomiting and sometimes loss of hair; greater exposure can cause sterility and cataracts and some forms of cancer and other diseases; severe exposure can cause death within hours. Hence this irradiation from excited neutrons and gamma rays is one of the greatest menaces for man and the biosphere as a whole.
Neutrons travel through the atmosphere at a speed in excess of 160,000 kilometers per second and gamma rays, which are of a shorter wavelength in respect to the rays that we can (optically) perceive, travel at the speed of light and therefore there is no way to avoid these radiations if exposed in the open since, practically at the same instant that the fireball is perceived, the percipient is already within a potentially lethal radiation field. While it is true that high yield weapons require time to release all their radiant energy, the energy release culminates within an insignificant lapse of time and practically the target area is immediately traversed by the emitted radiation. The only protection then would be a safety margin in respect to the distance from the explosion or a consistent screening with some high density material or within a properly adapted structure.

Shock and blast wave - A shock wave is a continuously propagated pressure pulse (or wave) in the surrounding medium which may be air, water, or earth, initiated by the expansion of the hot gases produced in an explosion. A shock wave in air is generally referred to as blast wave[1], because it resembles and is accompanied by strong, but transient, winds.

[1] For the purpose of this writing henceforward the term shock wave will be used whether the reference is to a low or to an high altitude explosion.