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High performance computing centres consume substantial amounts of energy to power large-scale supercomputers and the necessary building and cooling infrastructure. Recently, considerable performance gains resulted predominantly from developments in multi-core, many-core and accelerator technology. Computing centres rapidly adopted this hardware to serve the increasing demand for computational power. However, further performance increases in large-scale computing systems are limited by the aggregate energy budget required to operate them. Power consumption has become a major cost factor for computing centres. Furthermore, energy consumption results in carbon dioxide emissions, a hazard for the environment and public health; and heat, which reduces the reliability and lifetime of hardware components. Energy efficiency is therefore crucial in high performance computing.This chapter addresses key issues of energy-aware high performance computing. We outline some numerical methods which are often used in scientific applications, and present an energy profiling and tracing technique suitable to analyse the power consumption of applications. The next section is devoted to the performance and energy characterization of the sparse matrix-vector product, a basic numerical building block. Finally, we discuss opportunities for saving energy in computations by means of two examples. First, we present energy-aware runtimes on shared memory multi-core platforms for the Conjugate Gradient method. Second, we present energy-efficient techniques for multigrid methods on distributed memory clusters.