Invited review at the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, eds. J. Paul, T. Montmerle, and E. Aubourg; astro-ph/9911115

Abstract. I review the current status of studies of the large-scale structure of the Universe using redshift surveys of galaxies and clusters of galaxies. I first summarise the advances we have made in our knowledge of the cosmography of the z < 0.2 Universe during the last 25 years, as well as the status of the major surveys in progress. The question of how the a priori selection of some classes of objects biases the mapping of the underlying mass density field is discussed in some detail. I then emphasise the advantages of using clusters of galaxies selected in the X-ray band as tracers of large-scale structure, summarising the most recent results of the REFLEX survey, which is under completion. The strong potential of using X-ray clusters to study the evolution of structure to large redshifts is underlined. I then summarise some of the most recent statistical results on the clustering of galaxies and clusters, using the two-point correlation function (s) and the power spectrum P(k). In particular, I concentrate on the increased information available on the detailed shape of these functions on large scales, ~ 100 h^-1 Mpc. I argue that significant evidence is accumulating from different observations that the power spectrum has a well-defined and possibly narrow peak around k ~ 0.05 h Mpc^-1. In the near future, measures of P(k) from the full REFLEX survey, from the 2dF survey, and in particular from the SDSS large-volume subsamples will be crucial checks for these indications. I conclude with a glimpse into the future of large-scale structure surveys at high redshifts, describing the features of the VIRMOS deep survey, which will soon start collecting redshifts with the ESO VLT for ~ 150,000 galaxies at a typical depth of z = 1.

Table of Contents

INTRODUCTION

THE LARGE-SCALE GALAXY DISTRIBUTION WITHIN z 0.2

From 2D Photometric Galaxy Catalogues to Redshift Surveys

The Era of Multi-Object Spectroscopy

A FAIR SAMPLE OF THE UNIVERSE?

Density Fluctuations and Variances

Mapping Light, Mapping Mass

CLUSTERS OF GALAXIES AS TRACERS OF LARGE-SCALE STRUCTURE

The REFLEX Survey

STATISTICS OF LARGE-SCALE STRUCTURE

The Galaxy Two-Point Correlation Function

Redshift Space Distortions

The Large-Scale Shape of (r)

The Clustering of Clusters

The Power Spectrum

The Power Spectrum of the Galaxy Distribution

The Power Spectrum from Clusters

Features in the Power Spectrum

EVOLUTION OF LARGE-SCALE STRUCTURE

Non-Evolving Tracers?

Large Redshift Surveys to z ~ 1 and Beyond

X-ray Clusters as Tracers of High-z Structure

CONCLUSIONS

REFERENCES