Combinations of gradient plasticity with scalar damage and of gradient damage with isotropic plasticity are proposed and implemented within a consistently linearized format. Both constitutive models incorporate a Laplacian of a strain measure and an internal length parameter associated with it, which makes them suitable for localization analysis. The theories are used for finite element simulations of localization in a one-dimensional model problem. The physical relevance of coupling hardening/softening plasticity with damage governed by different damage evolution functions is discussed. The sensitivity of the results with respect to the discretization and to some model parameters is analyzed. The model which combines gradient-damage with hardening plasticity is used to predict fracture mechanisms in a Compact Tension test.