We review the quantitative science that can be and has been done with
redshift and peculiar velocity surveys of galaxies in the nearby unive
rse. After a brief background setting the cosmological context for thi
s work, the first part of this review focuses on redshift surveys. The
practical issues of how redshift surveys are carried out, and how one
turns a distribution of galaxies into a smoothed density held, are di
scussed. Then follows a description of major redshift surveys that hav
e been done, and the local cosmography out to 8,000 km s(-1) that they
have mapped. We then discuss in some detail the various quantitative
cosmological tests that can be carried out with redshift data. The sec
ond half of this review concentrates on peculiar velocity studies, beg
inning with a thorough review of existing techniques. After discussing
the various biases which plague peculiar velocity work, we survey qua
ntitative analyses done with peculiar velocity surveys alone, and fina
lly with the combination of data from both redshift and peculiar veloc
ity surveys. The data presented rule out the standard Cold Dark Matter
model, although several variants of Cold Dark Matter with more power
on large scales fare better. All the data are consistent with the hypo
thesis that the initial density field had a Gaussian distribution, alt
hough one cannot rule out broad classes of non-Gaussian models. Compar
ison of the peculiar velocity and density fields constrains the Cosmol
ogical Density Parameter. The results here are consistent with a flat
universe with mild biasing of the galaxies relative to dark matter, al
though open universe models are by no means ruled out.