The main focus of this talk will be on the way coalescents come down from infinity, and in particular on the asymptotic behavior of the number of blocks at small times. We show that it is given by the number of families alive at small times in a branching process. This approach casts a new light on recent results of Berestycki et al. and Bertoin and Le Gall which gave this behavior in special cases and connects in a unified way several recent results of Bertoin and Le Gall, Birkner et al., and Berestycki et al. (Based on joint works with N. Berestycki and J. Schweinsberg, N. Berestycki and V. Limic)