We discuss carefully the "blackbody approximation", stressing what it is (a limit case of radiative transfer), and what it is not (the assumption that the body is perfectly absorbing, namely "black"). Furthermore, we derive the Planck spectrum without enclosing the field in a box, as is done in most textbooks. Although convenient, this trick conceals the nature of the idealization expressed in the concept of a blackbody: first, the most obvious examples of approximate blackbodies, stars, are definitely not enclosed in boxes; second, the Planck spectrum is continuous, while the stationary modes of radiation in a box are discrete. Our derivation, although technically less elementary, is conceptually more consistent, and brings the opportunity to introduce to advanced undergraduate and graduate students the important concept of the "local density of states" via the resolvent formalism. (Contains 7 footnotes and 3 figures.)