Intelligent reflecting surfaces (IRSs) are revolutionary enablers for next-generation wireless communication networks, with the ability to customize the radio propagation environment. To fully exploit the potential of IRS-assisted wireless systems, reflective elements have to be jointly optimized with conventional communication techniques. However, the resulting optimization problems pose significant algorithmic challenges, mainly due to the large-scale non-convex constraints induced by the passive hardware implementations. In this paper, we propose a low-complexity algorithmic framework incorporating alternating optimization and gradient-based methods for large-scale IRS-assisted wireless systems. The proposed algorithm provably converges to a stationary point of the optimization problem. Extensive simulation results demonstrate that the proposed framework provides significant speedups compared with existing algorithms, while achieving a comparable or better performance.