The ever-increasing growth of the semiconductor market results in an increasing complexity of digital circuits. Smaller, faster, cheaper and low-power consumption are the main challenges in semiconductor industry. The reduction of transistor size and the latest packaging technology (i.e., System-On-a-Chip, System-In-Package, Trough Silicon Via 3D Integrated Circuits) allows the semiconductor industry to satisfy the latest challenges. Although producing such advanced circuits can benefit users, the manufacturing process is becoming finer and denser, making chips more prone to defects. The work presented in the HDR manuscript addresses the challenges of test and diagnosis of integrated circuits. It covers: - Power aware test; - Test of Low Power Devices; - Fault Diagnosis of digital circuits.