Eringen's micromorphic approach for materials with microstructure is applied to the plasticity and damage of single crystals. A plastic microdeformation variable and its rotational part are introduced in a standard crystal plasticity model in order to predict size effects in the overall stress response of crystalline solids. In the case of an ideal laminate microstructure including a purely elastic layer and a plastic layer undergoing single slip, the model, called microcurl, is shown to produce a kinematic hardening component that depends on the size of the layers. In a second part of the paper, a microdamage variable is introduced that accounts for cleavage or plasticity induced pseudo-cleavage phenomena in single crystals. The formulation accounts for straight crack paths but also allows for crack branching and bifurcation.