We are witnessing a revolution in our understanding of the structure, the history and the evolution of our Galaxy and Local Group galaxies thanks to the Gaia mission and the many wide angle photometric surveys conducted both from space and from the ground, as well as the spectroscopic surveys conducted mainly from the ground. The modelling of the stellar atmospheres and of their emerging radiation is crucial for the interpretation of the photometric and spectroscopic data already collected and that will be collected in the coming years.

There have been very important advances in the modelling of stellar atmospheres and their emerging spectra in the past ten years. The three-dimensional modelling of the stellar atmospheres has been tackled successfully in many cases. Line radiative transfer has been computed relaxing the assumption of Local Thermodynamic Equilibrium (LTE) for many atoms both in one-dimensional (1D) and three-dimensional (3D) model atmospheres.

The purpose of the Focus Meeting we propose, is to bring together the community that has been making these significant advances, often working in parallel. This will allow us to give to everybody an overview of the activities on these topics that are taking place in the different parts of the world, and an opportunity to build new synergies between the different groups.

Among the questions that we wish to tackle are: What developments do we need for non-LTE modelling ? What developments do we need for 3D model atmospheres ? How to efficiently compute large grids of model atmospheres and synthetic spectra (by large we mean more than 10^4 models/spectra ) ? How to validate the realism of synthetic spectra and colours ? What is the role of relatively small samples of stars with extremely high quality observations ? How to best extract astrophysical information from extremely large collections of data ?

We wish to dedicate this Focus Meeting to the memory of Fiorella Castelli, who has greatly contributed to these topics.