>>10891992A military-type CBRN filter has two basic components: a particulate filter and a chemical filter. The particulate filter removes particles like dust, bacteria, and viruses. There are different ways to build particulate filters, but the end result is a stack of material with very small holes that the air passes through. The holes are smaller than the particles, so the particles stay on the outside. Different filters have different ratings based on the size of particles they can exclude and their efficiency.
The chemical filter is used to remove reactive gases and consists of a bed of activated carbon. The activated carbon is both highly absorbent and highly reactive, so the chemicals get trapped or react and produce less harmful products. The carbon has a very limited capacity, after which point the harmful gases will pass through unaffected. That's why filters have to be kept sealed before use, have a limited shelf life, and need to be changed every few hours when in use.
Gas mask filters don't stop radiation, but the particulate filter does stop radioactive dust.