Redshift surveys of the local Universe show how galaxy clusters lie at the nodes of a cosmic web. N-body simulations of dark matter dominated universes show that the gravitational instability hypothesis succeeds at reproducing the gross features of the large-scale structure today. In these simulations, clusters form by accreting smaller clumps of dark matter along preferred directions and the cluster assembly is far from proceeding smoothly and isotropically. Direct examination of this hierarchical clustering process remains fertile ground for both observation and theory.

Galaxies in clusters are substantially different from galaxies in the field. The strong correlation of optical and radio properties of galaxies with their environment indicates that the formation and evolution of galaxies is intimately linked to the formation of large-scale structure. Evidence of this link should be present in the regions intermediate between the central cores of clusters and the surrounding large-scale structure.

Until recently, observational limitations have limited studies of the outskirts of clusters. During the last few years, (1) intense observation of the external regions of nearby clusters (e.g. the CAIRNS survey), and (2) wide-field optical imaging at moderately high redshifts have come of age. At moderate redshifts wide-field imaging and spectroscopy on many telescopes (including those of the 8-10 meter class, e.g. Suprime-Cam on the Subaru telescope), have dramatically made  the outskirts of clusters much more accessible to observation. These data have begun to shed light on the connection between large-scale structure formation and galaxy evolution. Indeed recent optical and near-infrared observations clearly indicate that the external regions of galaxy clusters at both low and moderate redshift (z~0.4) contain galaxies with intermediate properties between the red galaxies core population and the star-forming blue galaxies in the field. Coupled with deeper theoretical investigations, these data may discriminate among the many processes which may contribute to spectroscopic and morphological transformation of galaxies.

In addition to being a site of galaxy evolution, the outskirts of clusters may be a reservoir for a warm intergalactic medium. The baryon budget of the Universe, derived by combining the measurements of the light element abundances with the amount of hot gas in galaxy clusters, indicates that most baryons should be in a warm intergalactic medium component, with a temperature in the range 10⁴-10⁶ K.  Despite the  challenge of the observations, detection of this warm gas,  first positied on theoretical grounds, was recently reported. This gas should contain information on the energy and heavy elements ejected by galaxies: the knowledge of its properties is crucial for designing realistic models of galaxy formation.

Current large redshift surveys (2dF, SDSS) and upcoming optical deep surveys (e.g. Virmos-VLT Deep Survey, DEEP2 survey) will provide a wealth of data on galaxies in the external regions of clusters. Moreover, with wide-field multi-object spectroscopy (e.g. on the MMT or on the Magellan 6.5m with the coming IMACS spectrograph) one can obtain more than a thousand spectra per mask, probing with unprecedent accuracy the dynamics of the infall regions of clusters at both low and high redshift.

Properties of the hot and warm baryon contents of clusters and its surroundings will be measured by (1) high-sensitivity, high-angular resolution X-ray telescopes (e.g. XMM), and (2) wide field surveys in the microwave bands aimed at detecting clusters with the Sunyaev-Zeldovich effect; this effect has the advantage of being more sensitive than X-ray observations to the external regions of clusters.

Both the central regions of galaxy clusters and the large-scale distribution of galaxies in the Universe have been the topics of many dedicated conferences for the last two decades. In contrast, little attention has been devoted to the outskirts of clusters. This topic is currently going through a period of exciting discoveries and, in the coming years, it is likely to become increasingly important in the cosmology and galaxy formation research fields.

We therefore believe that it is a perfect time to gather the scientists active in the field of galaxy and cluster formation (1) to discuss the observational multi-wavelength data currently available on the external regions of clusters, and (2) to investigate future strategies necessary to unveil the many processes which connect the formation of the large-scale structure to galaxy formation and evolution.