CP stars are stage to a diversity of physical phenomena. Instruments are  now able to deliver data with unprecedented signal-to-noise and spectral  resolution, providing a unique opportunity to study these physical  processes in detail and their impact on stellar structure and evolution.
However, while recent data have generated astonishing results in this  field of research, they have also raised important issues that need to  be investigated with particular care. In fact, spectral lines of some CP  stars yield a zoo of 3-D information and it is urgent to learn to  disentangle the signatures left by the different physical phenomena, and  particularly their 3-D and time-dependent structures.

Diffusion and chemical stratification
The diffusion process, which is believed to be the main cause of  abundance peculiarities in CP stars, can affect their structure and  evolution. It is now understood that in some stars elemental abundances  change by several orders of magnitude within the line-forming region.  The chemical segregation is responsible for some of the atmospheric and  spectral anomalies that puzzled astronomers for many decades.
The stratification of chemical elements and, particularly, the  accumulation or depletion of some elements in the uppermost layers of CP  atmospheres, also highlights the necessity to take into account  departures from local thermodynamics equilibrium (LTE). Although much  progress has been made recently, non-LTE modelling of CP stars still  needs stratified model atmospheres and more accurate atomic data, in  particular collisional cross-sections and photoionization cross-sections.

Magnetic fields
The upper main sequence CP stars are also privileged astrophysical  laboratories for investigation of stellar magnetism. Thanks to the large  strength and relatively simple geometry of the CP-star fields, these objects remain by far the most numerous and thoroughly studied class of  magnetic stars. Unique observational material, interpreted with novel  modelling techniques such as magnetic Doppler imaging, allow us to construct assumption-free maps of magnetic fields on the stellar  surface. These state-of-the-art magnetic maps have revealed that the  fields in CP stars deviate from the  simple low-order multipolar  geometries, and contain small-scale structures. These  discoveries  directly challenge existing theories of the formation and evolution of magnetic fields in the upper main sequence.

Pulsations
High-resolution spectroscopic time series have allowed us to probe  directly the dynamics of the pulsations in the atmospheres of rapidly  oscillating Ap (roAp) stars, and to discover links between the pulsation  properties, the structure of the magnetic field and the horizontal  patches and vertical stratification of chemical elements. Such links  are revealed, for instance, in running waves, a phenomenon similar to  that observed in regions of strong magnetic field of the solar atmosphere.
One particularly exciting outcome of the study of these oscillations is  that they can, in principle, provide a direct link between the physical height in the atmosphere and the height at which the lines used to  observe the pulsations are formed. On the other hand, vertical mapping of stellar atmospheric chemistry complements horizontal mapping of starspots with the Doppler imaging technique. A combination of the two techniques, aided by the tomography of stellar p-mode pulsations, promises to deliver remarkable 3-D maps of CP-star atmospheres. To achieve that, a detailed comparison between the outcome of the models describing the pulsations and the spectroscopic data is still needed. As the models depend strongly on the magnetic-field topology, information about the latter can also be retrieved from such a comparison.

Convection
Many important physical questions concerning CP stars are related to convection. The line profiles of some (mostly, but not exclusively) Am stars are characterized by unusual shapes, currently modelled with macroturbulence. Deeper in the envelope of Am stars, the possible interaction of convection with diffusion caused by accumulation of iron-peak elements needs also to be further explored.
The degree to which magnetic fields might suppress turbulence in the envelope and atmosphere of Ap-stars also remains an open question at present. On the one hand, suppression of convection is required to successfully explain the excitation of the rapid oscillations observed in roAp stars. On the other, macroturbulent broadening has recently been suggested to explain some peculiarities of their line profiles.
Last, but not least, numerical simulations of convective cores of A-stars suggest a possible dynamo operating in their interiors. These and other recent results pointing to fossil fields as the natural explanation for the magnetism of Ap stars, bring new light to the long-lasting debate about the origin and evolution of magnetic fields in these stars.

A look into the future
Most of the exciting results from high spectral- and time-resolution spectroscopy and spectropolarimetry of various subgroups of CP stars are very recent. New discoveries are being made at a rapid rate, and challenges are constantly being posed to those carrying out theoretical studies. While these are expected to continue throughout the coming years, different new instruments, such as ASTRA, CRIRES*,* CoRoT, Kepler, GAIA and WSO-UV, are, or will become available soon, and will open new windows for studies of CP stars.During this meeting many new results from high-quality data and sophisticated theoretical models will be presented. We will discuss the techniques used to infer the data, and the ingredients of the models with which the data is compared. Particular emphasis will be given to the limitations of the available tools and ways to minimize or even overcome these limitations. Future challenges, expected in the context of new ground-based instrumentation, and of space missions recently launch or in preparation, will give the final tone to the Joint Discussion.