Test cost has become a significant portion of device cost and a bottleneck in high volume manufacturing. Increasing integration density and shrinking feature sizes increased test time/cost and reduce observability. Test engineers have to put a tremendous effort in order to maintain test cost within an acceptable budget. Unfortunately, there is not a single straightforward solution to the problem. Products that are tested have several application domains and distinct customer profiles. Some products are required to operate for long periods of time while others are required to be low cost and optimized for low cost. Multitude of constraints and goals make it impossible to find a single solution that work for all cases. Hence, test development/optimization is typically design/circuit dependent and even process specific. Therefore, test optimization cannot be performed using a single test approach, but necessitates a diversity of approaches. This works aims at addressing test cost minimization and test quality improvement at various levels. In the first chapter of the work, we investigate pre-silicon strategies, such as design for test and pre-silicon statistical simulation optimization. In the second chapter, we investigate efficient post-silicon test strategies, such as adaptive test, adaptive multi-site test, outlier analysis, and process shift detection/tracking.