Today's IC design is facing several challenges due to increasing circuit complexity and decreasing feature size, as it pushes to extend Moore's law into nano-scale dimensions. Apart from the challenges that arise directly as a result of feature scaling (e.g., increasing leakage power, reliability issues), imperfections in the manufacturing process have recently turned into a major design hurdle, due to the variations they cause in the device and interconnect parameters from their target values. From an IC design automation perspective, a shift in paradigm, from deterministic to probabilistic, is needed to handle the unpredictable nature of these fabrication variations. In such a probabilistic paradigm, the varying circuit parameters such as leakage power or delay should be accurately modeled, and their correlations due to common sources of variations or physical location on the chip should be well captured. Moreover, variability-driven (probabilistic) design automation needs to efficiently generate a high quality solution. A particular challenge in variability-driven design automation is to define optimality measures among candidate solutions, which allow for inferior solutions to be removed from the solution space thus reducing the run-time complexity. In this dissertation, the superiority probability is introduced as such an optimality measure, and two methods are proposed to compute this probability: an accurate Conditional Monte Carlo simulation method, and an efficient moment-matching approximation method. The effectiveness of using the superiority probability is shown in the context of two important design automation applications: 1) the buffer insertion problem, 2) the dual-Vth leakage optimization problem. Another important task in variability-driven design automation is to develop optimization techniques that can provably generate the optimal solution in an efficient way. In this dissertation, the application of the gate sizing problem is explored to optimally reduce the loss due to fabrication variations in the presence of a timing constraint. The presented formulation, in contrast with the existing variability-driven approaches which are all based on heuristics, is provably optimal. Moreover, unlike existing approaches, it is independent of any assumption on the source and nature of variations.