  We give a summary of recent results on spatial and velocity biases in
cosmological models. Progress in numerical techniques made it possible to
simulate halos in large volumes with a such accuracy that halos survive in
dense environments of groups and clusters of galaxies. Halos in simulations
look like real galaxies, and, thus, can be used to study the biases --
differences between galaxies and the dark matter. The biases depend on scale,
redshift, and circular velocities of selected halos. Two processes seem to
define the evolution of the spatial bias: (1) statistical bias and (2) merger
bias (merging of galaxies, which happens preferentially in groups, reduces the
number of galaxies, but does not affect the clustering of the dark matter).
There are two kinds of velocity bias. The pair-wise velocity bias is
b_12=0.6-0.8 at r< 5Mpc/h, z=0. This bias mostly reflects the spatial bias and
provides almost no information on the relative velocities of the galaxies and
the dark matter. One-point velocity bias is a better measure of the velocities.
Inside clusters the galaxies should move slightly faster (b_v =1.1-1.3) than
the dark matter. Qualitatively this result can be understood using the Jeans
equations of the stellar dynamics. For the standard LCDM model we find that the
correlation function and the power spectrum of galaxy-size halos at z=0 are
antibiased on scales r<5Mpc/h and k=(0.15-30)h/Mpc.
