Intelligent reflecting surfaces (IRSs) are emerging as promising enablers for the next generation of wireless communication systems, because of their ability to customize favorable radio propagation environments. However, with the conventional passive architecture, IRSs can only adjust the phase of the incident signals limiting the achievable beamforming gain. To fully unleash the potential of IRSs, in this paper, we consider a more general IRS architecture, i.e., active IRSs, which can adapt the phase and amplify the magnitude of the reflected incident signal simultaneously with the support of an additional power source. To realize green communication in active IRS-assisted multiuser systems, we jointly optimize the reflection matrix at the IRS and the beamforming vector at the base station (BS) for the minimization of the BS transmit power. The resource allocation algorithm design is formulated as an optimization problem taking into account the maximum power budget of the active IRS and the quality-of-service (QoS) requirements of the users. To handle the non-convex design problem, we develop a novel and computationally efficient algorithm based on the bilinear transformation and inner approximation methods. The proposed algorithm is guaranteed to converge to a locally optimal solution of the considered problem. Simulation results illustrate the effectiveness of the proposed scheme compared to the two baseline schemes. Moreover, the results unveil that deploying active IRSs is a promising approach to enhance the system performance compared to conventional passive IRSs, especially when strong direct links exist.