The blackbody radiation field is studied from different points of view. The existence of zero-point fluctuations is shown to be crucial in determining the form of the thermal part of the spectrum. The notion of a continuous field is seen to be compatible with a discrete structure for its interaction: The description normally used in the quantum context does not refer to the field but to its interaction with atomic systems, which involves statistically independent elementary acts of absorption and emission. (...) The same classical field has different effects on absorption and on emission, and these are conveniently, but not necessarily, described in terms of non-commuting operators. (shrink)