I review the insights emerging from recent large kinematic surveys of galaxies at low redshift, with particular reference to the SAMI, CALIFA and MaNGA surveys. These new observations provide a more comprehensive picture of the angular momentum properties of galaxies over wide ranges in mass, morphology and environment in the present-day universe. I focus on the distribution of angular momentum within galaxies of various types and the relationship between mass, morphology and specific angular momentum. I discuss the implications of the new results for models of galaxy assembly.