A typical stellar spectrogram shows a vast number of spectral lines. Each of these has its characteristic shape and strength which must, in some way, reflect the structure of the atmosphere in which the radiation arose. It seems reasonable that from all this profile data we should be able (and with considerable redundancy) to infer a good deal about the physical structure of the radiating gas, and a major effort has correspondingly been devoted to clarifying the physical basis of spectral line formation, i.e., exactly how the atmospheric structure and the atomic properties are reflected in the line profiles. This problem, however, is far from solved : Few, if any, of the profiles of strong lines can be predicted in detail from model atmospheres, nor have analyses of the profiles yielded unambiguous data on the atmospheric structure. Indeed, as recently as 1967, the participants at a conference in Bilderberg (Holland) concluded that no data at all which had been obtained from line profile analyses was worthy of inclusion in specifying the solar atmospheric model. Evidently, then, the problem of line formation is not trivial ; in this paper we discuss some of the difficulties and review the not inconsiderable progress which has been made in this area of astrophysical research.