In complex plasmas, dust particles are charged through their interactions with the electrons and ions of the surrounding plasma. In low-temperature laboratory plasmas, dust particles most commonly acquire a negative charge. In particular, in a laboratory glow-discharge plasma, the typical charge for a micrometer-size grain generally attains a few thousands of electronic charges. Under stable discharge conditions, this large negative charge is relatively well-characterized. However, for unsteady discharge conditions, the charge can differ and even fluctuate. In particular, when the power source of the discharge is turned off, the charged species of the plasma diffuse away and recombine into neutral species: this is a temporal afterglow. When dust particles are present inside a temporal plasma afterglow, the diffusion of charged species and the plasma decay dynamics are affected. Moreover, the dust particle charges also evolve during the afterglow period. In the late afterglow, dust particles are known to keep residual charges. The value of these residual charges strongly depends on the ambipolar-to-free diffusion transition. In addition, the presence of a constant electric field, causing ions to drift through the neutral gas, has a strong influence on the final dust particle residual charges, eventually leading to large positive residual charges. In this review article, the dynamics of temporal complex plasma afterglow are discussed. Experimental and theoretical results are presented. The basics of temporal afterglow modeling are also given.