A selection of surface crack problems is presented to provide insights into Stage I and early Stage II fatigue crack growth. Edge cracks at 45 o and 90 o to the surface are considered for cracks growing in single crystals. Both single crystal slip and conventional plasticity are employed as constitutive models. Edge cracks at 45 o to the surface are considered that either (i) kink in the direction perpendicular to the surface, or (ii) approach a grain boundary across which only elastic deformations occur.