  Understanding the formation and evolution of large-scale structure is a
central problem in cosmology and enables precise tests of General Relativity on
cosmological scales and constraints on dark energy. An essential ingredient is
an accurate description of the pairwise velocities of biased tracers of the
matter field. In this paper we compute the first and second moments of the
pairwise velocity distribution by extending the Convolution Lagrangian
Perturbation theory (CLPT) formalism of Carlson et al. (2012). Our predictions
outperform standard perturbation theory calculations in many cases when
compared to statistics measured in N-body simulations. We combine the CLPT
predictions of real-space clustering and velocity statistics in the Gaussian
streaming model of Reid & White (2011) to obtain predictions for the monopole
and quadrupole correlation functions accurate to 2 and 4 per cent respectively
down to <25Mpc/h for halos hosting the massive galaxies observed by SDSS-III
BOSS. We also discuss contours of the 2D correlation function and clustering
"wedges". We generalize the scheme to cross-correlation functions.
