  We study shrinking targets problems for discrete time flows on a homogenous
space $\Gamma\backslash G$ with $G$ a semisimple group and $\Gamma$ an
irreducible lattice. Our results apply to both diagonalizable and unipotent
flows, and apply to very general families of shrinking targets. As a special
case, we establish logarithm laws for cusp excursions of unipotent flows
answering a question of Athreya and Margulis.
