Managing the power consumption of circuits and systems is now considered as one of the most important challenges for the semiconductor industry. Elaborate power management strategies, such as voltage scaling, clock gating or power gating techniques, are used today to control the power dissipation during functional operation. The usage of these strategies has various implications on manufacturing test, and power-aware test is therefore increasingly becoming a major consideration during design-for-test and test preparation for low power devices. This tutorial provides knowledge in this area. It is organized into three main parts. The first one gives necessary background and discusses issues arising from excessive power dissipation during test application. The second part provides comprehensive knowledge of structural and algorithmic solutions that can be used to alleviate such problems. The last part surveys low power design techniques and shows how these low power devices can be tested safely without affecting yield and reliability. EDA solutions for considering power during test and design-for-test are also discussed in the last part of the tutorial.