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The connection recently found between bars and dark matter haloes opens the possibility of indirectly assessing the physical properties of haloes through the observed properties of bars within them. With this aim, one first needs to make a detailed comparison between real and simulated bars. If simulations can successfully reproduce the structural properties of barred galaxies, then they might indeed give us useful estimates of physical properties of real haloes, via comparisons of observations of barred galaxies to models with known halo properties. Such a project has been started (see [37]), and preliminary results are encouraging: n-body snapshots are being used as real galaxy images as input to BUDDA, and a careful comparison of the structural parameters so obtained with those of real barred galaxies shows that simulations are able to generally reproduce the observed quantities.

It is evident the need of further work on the methodology to estimate the dynamical ages of bars. I already mentioned above some possible ways in this direction, and the need to enlarge the sample for which this parameter is measured. Another important parameter that has to be measured for larger samples is the bar pattern speed (see e.g. [43, 77, 91]). Models of bar formation and evolution make clear predictions on the behaviour of this parameter, which seems to be related to a number of other physical properties: the central concentration of the dark matter halo, the exchange of angular momentum between disc and halo, bar age, and even bar generation. It will be very useful to have estimates, for a large sample, of both bar age and pattern speed.

On the theory side, it is important now to obtain an updated criterion for the onset of the bar instability in discs, accounting for the role of the halo. This will be very useful for semi-analytic models (see [67]) which consider bar instability based on earlier studies. Such models can also benefit largely from detailed prescriptions for the transport of disc material to the centre, and the building of disc-like and box/peanut bulges. It is only recently that n-body simulations dedicated to study the formation and evolution of bars started to use responsive, cosmologically motivated haloes, and it is naturally expected that significant progress will come from such studies. Finally, the observed dichotomy between bars in early and late type disc galaxies has to be better understood. It is very likely that the availability of a large gas content in the disc plays a key role. Theoretical work focused on the effects of gas in bar formation and evolution can substantially improve our understanding on this subject.

Acknowledgment. I am very grateful to the organisers, in particular Nikos Voglis and Panos Patsis, for this wonderful opportunity. I benefitted from discussions with several authors, especially Lia Athanassoula and Peter Erwin. I thank Guinevere Kauffmann for letting me present here previously unpublished results from our structural analysis of SDSS images. Comments from the reviewer, Preben Grosbøl, were greatly appreciated and helpful to improve this paper. The author is supported by the Deutsche Forschungsgemeinschaft priority program 1177 ("Witnesses of Cosmic History: Formation and evolution of galaxies, black holes and their environment"), and the Max Planck Society.

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