The axino, the fermionic superpartner of the axion, is a well-motivated candidate for cold dark matter if it is the lightest supersymmetric particle. Since the axino couples very weakly to the matter multiplets, the next-to-lightest supersymmetric particle (NLSP) has a long lifetime, which has important consequences for both cosmology and collider phenomenology. Assuming that a charged slepton is the NLSP, we calculate the complete leading one- and two-loop contributions to its decay. We analyze in detail constraints on the parameter space from cosmology and discuss how this scenario can be probed at colliders. Scenarios in which both the axino and the gravitino are lighter than the long-lived charged slepton are also explored with particular emphasis on cosmological constraints and collider phenomenology.