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Looking at the various topics addressed in this paper, we can probably imagine the future development of this field during the first 10 years of the new Millennium as possibly moving along two directions.

One one side, the completion of the 2dF and in particular of the Sloan Digital Sky Survey will produce profound progress in the knowledge of many important statistical aspects of large-scale structure at z ~ 0. First of all, it is clear that something very interesting is hidden in the exact shape of the power spectrum near the expected turnover. While we seem finally to detect such turnover with some significance from the best samples now available, the data are still too poor on scales of 500 - 1000 h-1 Mpc to sample it with sufficient resolution in k space. This feature is more clearly detected when high-threshold objects as clusters of galaxies or Lyman-break galaxies are analysed. Larger samples of clusters of galaxies will be therefore essential: the REFLEX survey will be pushed down in flux by about a factor of two within the next two years, which will bring the number of clusters in the sample up to ~ 800, probing a volume extending to z ~ 0.3. At the same time, the sample of red luminous galaxies from the SDSS seems to represent the most promising data set for exploring the scales around the peak of P(k) in sufficient detail. Also, the question on whether these features in the distribution of objects are partly a product of biasing, and therefore cannot be transferred to the matter power spectrum, will find an answer when detailed CMB anisotropy experiments will explore such scales. There seem to be all premises that the Planck Surveyor (see e.g. Efstathiou, these proceedings) will be able to provide this information to a high level of accuracy.

At the same time, 10-meter class telescopes equipped with a new generation of spectrographs give the opportunity to extend systematic studies of large samples of galaxies to redshifts above unity. I have briefly described the largest of these projects, the VLT-VIRMOS deep survey. Similar surveys with smaller sizes are being planned by different groups around the World, as newer instrumentation on very large telescopes commences operation. One example that I did not have time to discuss here is the Deimos spectrograph, under construction for the Keck II telescope [139].

The study of very large volumes of the Universe at high redshifts, however, will have to resort to using tracers which can be both more efficient and easier to understand than galaxies. X-ray selected clusters of galaxies provide this opportunity. Consequently, it would be highly significant if within the next ~ 10 years a large, possibly all-sky, survey in the X-ray band to a flux about 2 orders of magnitude fainter than the ROSAT All-Sky Survey (~ 10-14 erg s-1 cm-2) be performed. Concrete proposals in this direction have recently been presented [136], and will hopefully become reality in the near future.


I would like to thank the organizers of the 19th Texas Symposium on Relativistic Astrophysics for inviting me to give this review talk. I thank all my collaborators in the large-scale structure projects I have described throughout this paper, particularly Hans Böhringer, Guido Chincarini, Chris Collins, Olivier Le Févre, Peter Schuecker, Paolo Vettolani and Elena Zucca. A special acknowledgment goes to Stefano Borgani for a number of enlightening discussions on the use of X-ray clusters as tracers of large-scale structure, for teaching me a lot about theoretical cosmology and for reading the manuscript. Thanks are due also to Fiona Hoyle, Helen Tadros, Matthew Colless and Huan Lin for providing electronic versions of their results and to Silvia Quarello for useful discussions. I am also grateful to Rychard Bouwens for carefully reading an early version of the manuscript and providing useful comments.

Finally, special thanks should go to my wife and my kids, for their patience during the hours spent writing this review during weekends, and for alleviating the difficulty of finishing it, through their company and background playing.

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