This review examines the principles, limitations, and recent advancements in elastic modulus measurement using nanoindentation. The importance of accurate contact area prediction is discussed, along with the Oliver-Pharr method and its limitations. The Continuous Stiffness Measurement (CSM) technique is presented as a significant improvement, allowing continuous measurement of mechanical properties throughout the indentation process. For ultra-thin films, the Li and Vlassak method, which incorporates Yu's solution and the concept of effective thickness, is highlighted as a means to correct for substrate effects. Recent developments in artificial neural network-based models for elastic modulus prediction are also explored. These advancements have greatly expanded the applicability of nanoindentation in semiconductor and MEMS device reliability assessment.