Sample-spanning networks of aggregated colloidal particles have a finite stiffness and deform elastically when subjected to a small shear stress. After some period of creep, these gels ultimately suffer catastrophic failure. This delayed yielding is governed by the association and dissociation dynamics of interparticle bonds and the strand structure of the gel. We derive a model which connects the kinetics of the colloids to the erosion of the strand structure and ultimately to macroscopic failure. Importantly, this model relates time-to-failure of the gel to an applied static stress. Model predictions are in quantitative agreement with experiments. It is predicted that the strand structure, characterized by its mesh size and strand coarseness, has a significant impact on delay time. Decreasing the mesh size or increasing the strand thickness makes colloidal gels more resilient to delayed yielding. The quench and flow history of gels modify their microstructures. Our experiments show that a slow quenching increases the delay time due to the coarsening of the strands; by contrast, preshear reduces the delay time, which we explain by the increased mesh size as a result of shear-induced fracture of strands.