Graphics processing units (GPUs) provide an order-of-magnitude improvement on peak performance and performance-per-watt as compared to traditional multicore CPUs. However, GPU-accelerated systems currently lack a generalized method of power and performance prediction, which prevents system designers from an ultimate goal of dynamic power and performance optimization. This is due to the fact that their power and performance characteristics are not well captured across architectures, and as a result, existing power and performance modeling approaches are only available for a limited range of particular GPUs. In this paper, we present power and performance characterization and modeling of GPU-accelerated systems across multiple generations of architectures. Characterization and modeling must be tightly coupled to conclude what GPUs can optimize power and performance, and how they are predictable. We quantify impact of voltage and frequency scaling on each architecture with a particularly intriguing result that a cutting-edge Kepler-based GPU achieves energy saving of 75% by lowering GPU clocks in the best scenario, while Fermi- and Tesla-based GPUs achieve no greater than 40% and 13%, respectively. Considering these characteristics, we provide statistical power and performance modeling of GPU-accelerated systems simplified enough to be applicable for multiple generations of architectures. Our finding is that even simplified statistical models are able to predict power and performance of cutting-edge GPUs within errors of 20% to 30% for any set of voltage and frequency.