We investigate theoretically light- and bias-induced metastabilities in Cu(In,Ga)Se2 (CIGS) based solar cells, suggesting the Se-Cu divacancy complex (VSe-VCu) as the source of this hitherto puzzling phenomena. Due to its amphoteric nature, the (VSe-VCu) complex is able to convert by persistent carrier capture or emission from a shallow donor into a shallow acceptor configuration, and vice versa, thereby changing in a metastable fashion the local net acceptor density inside the CIGS absorber of the solar cell, e.g., a CdS/CIGS heterojunction. In order to establish a comprehensive picture of metastability caused by the (VSe-VCu) complex, we determine defect formation energies from first-principles calculations, employ numerical simulations of equilibrium defect thermodynamics, and develop a model for the transition dynamics after creation of a metastable nonequilibrium state. We find that the (VSe-VCu) complex can account for the light-induced metastabilities, i.e., the ``red'' and ``blue'' illumination effects, as well as for the reverse-bias effect. Thus, our (VSe-VCu) model implies that the different metastabilities observed in CIGS share a common origin. A defect state in the band gap caused by (VSe-VCu) in the acceptor configuration creates a potentially detrimental recombination center and may contribute to the saturation of the open circuit voltage in larger-gap Cu(In,Ga)Se2 alloys with higher Ga content. Therefore, the presence of metastable defects should be regarded as a concern for solar cell performance.