With each technology generation, the effects of on-chip variations are seen to more profoundly affect digital circuit behavior. These variations may arise from fluctuations attributed to the manufacturing process (e.g., drifts in channel length, oxide thickness, threshold voltage, or doping concentration), which affect the circuit yield, as well as variations in the environmental operating conditions (e.g., supply voltage or temperature) after the circuit is manufactured, which impact the performance of the design. These effects can cause unacceptable alterations in circuit performance parameters such as timing and power, and variation-tolerant design is imperative for next-generation designs. This paper overviews research in this area, describing methods for the analysis and optimization of statistical effects.