  I review here past and present research on clusters and groups of galaxies
within the Sloan Digital Sky Survey (SDSS). In particular, I discuss the C4
algorithm which is designed to search for clusters within a 7-dimensional
data-space, i.e., simultaneous in both color & space. The C4 catalog has a well
defined selection function based on mock SDSS galaxy catalogs constructed from
the Hubble Volume simulation, and is >90% complete, with <10% contamination,
for halos with M200 > 10^14 Msolar at z<0.14. Furthermore, the observed summed
r-band luminosity of C4 clusters is linearly related to M200 with <30% scatter
at any given halo mass. I also briefly review the selection and observation of
Luminous Red Galaxies (LRGs) and demonstrate that these galaxies have a similar
clustering strength as clusters and groups of galaxies. I outline a new
collaboration planning to obtain redshifts for 10,000 LRGs at 0.4<z<0.7 using
the SDSS photometric data and the AAT 2dF instrument. Finally, I review the
role of clusters and groups of galaxies in the study of galaxy properties as a
function of environment. In particular, I discuss the ``SFR--Density'' and
``Morphology--Radius'' relations for the SDSS and note that both of these
relationships have a critical density (or ``break'') at a projected local
galaxy density of ~1 h_75^2 Mpc^-2 (or between 1 to 2 virial radii). One
possible physical mechanism to explain this observed critical density is the
stripping of warm gas from the halos of in-falling spiral galaxies, thus
leading to a slow strangulation of star-formation in these galaxies. This
scenario is consistent with the recent discovery (within the SDSS) of an excess
of ``Passive'' or ``Anemic'' spiral galaxies located within the in-fall regions
of C4 clusters.

Astrophysics