Published online by Cambridge University Press: 22 April 2008
In the last years, some issues concerning Cepheids have beenresolved, based on observations and modeling. However, as usual, newdifficulties arise. The link between the dynamical structure ofCepheid atmosphere and the distance scale calibration in theuniverse is now clearly established. To support observations, wecurrently need fully consistent hydrodynamical models, includingpulsating and evolutionary theories, convective energy transport,adaptive numerical meshes, and a refined calculation of theradiative transfer within the pulsating atmosphere, and also in theexpected circumstellar envelope (hereafter CSE). Confronting suchmodels with observations (spectral line profiles, spatial- andspectral- visibility curves), will permit to resolve and/orstrengthen subtle questions concerning (1) the limb-darkening, (2)the dynamical structure of Cepheids' atmosphere, (3) the expectedinteraction between the atmosphere and the CSE, and (4) it willbring new insights in determining the fundamental parameters ofCepheids. All these physical quantities are supposed furthermore tobe linked to the pulsation period of Cepheids. From these studies,it will be possible to paint a glowing picture of all Cepheidswithin the instability strip, allowing an unprecedent calibration ofthe period-luminosity relation (hereafter PL relation),leading to new insights in the fields of extragalactic distancescales and cosmology.