Modern graphics processing units (GPUs) have complex architectures that admit exceptional performance and energy efficiency for high-throughput applications. Although GPUs consume large amounts of power, their use for high-throughput applications facilitate state-of-the-art energy efficiency and performance. Consequently, continued development relies on understanding their power consumption. This work is a survey of GPU power modeling and profiling methods with increased detail on noteworthy efforts. As direct measurement of GPU power is necessary for model evaluation and parameter initiation, internal and external power sensors are discussed. Hardware counters, which are low-level tallies of hardware events, share strong correlation to power use and performance. Statistical correlation between power and performance counters has yielded worthwhile GPU power models, yet the complexity inherent to GPU architectures presents new hurdles for power modeling. Developments and challenges of counter-based GPU power modeling are discussed. Often building on the counter-based models, research efforts for GPU power simulation, which make power predictions from input code and hardware knowledge, provide opportunities for optimization in programming or architectural design. Noteworthy strides in power simulations for GPUs are included along with their performance or functional simulator counterparts when appropriate. Last, possible directions for future research are discussed.