With the concerted efforts from researchers in hardware, software, algorithm, and data management, HPC is moving towards extreme-scale, featuring a computing capability of quintillion (10 18 ) FLOPS. As we approach the new era of computing, however, several daunting scalability challenges remain to be conquered. Delivering extreme-scale performance will require a computing platform that supports billion-way parallelism, necessitating a dramatic increase in the number of computing, storage, and networking components. At such a large scale, failure would become a norm rather than an exception, driving the system to significantly lower efficiency with unprecedented amount of power consumption.To tackle this challenge, we propose an adaptive and power-aware algorithm, referred to as Lazy Shadowing, as an efficient and scalable approach to achieve high-levels of resilience, through forward progress, in extreme-scale, failure-prone computing environments. Lazy Shadowing associates with each process a "shadow" (process) that executes at a reduced rate, and opportunistically rolls forward each shadow to catch up with the its leading process during failure recovery. Compared to existing fault tolerance methods, our approach can achieve 20% energy saving with potential reduction in solution time at scale.