Metrology is the science of measurement. It is necessary for the development of new processes, the control and monitoring of existing ones, and as a product qualification yardstick. Microscopes are widely used to make precise distance measurements. They are especially important in the semiconductor industry where critical dimensions (CDs) are rapidly approaching 0.1 pm. The requirement in integrated circuit metrology that the fabrication tolerance be 10% of the critical dimension translates to a demanded measurement precision (between 10 - 40 % of the fabrication tolerance) on the single nanometer level. For example, the fabrication tolerance for a 0.25 pm nominal gate length would be 0.025 pm and the metrology precision around 0.0025 pm, or 2.5 nm - about five atoms long ! Similar arguments can be made for the relative (overlay) and absolute (placement) position of the feature as well. These metrology requirements were based upon a 10% rule and a new criterion or modification of this rule may have to be applied to the metrology requirements as the dimensions to be measured approach the nanometer scale. Submicrometer device fabrication metrology also involves performing measurements in three dimensions. Masks and wafers contain features with high aspect ratios and are composed of multiple layers of different materials; both factors make the theory and understanding of the metrology tool behavior complicated. In addition to measuring submicrometer feature dimensions and placements with nanometer-scale precision, high throughput and full automation are also desirable for an in-line manufacturing implementation. In this chapter, we will mainly be concerned with dimensional metrology of lithographic masks and patterned semiconductor wafer features after processing (post-fabrication); in particular, the measurement of feature width, height (depth), overlay, and placement. Because the theoretical limits of measurement capability are being approached, it is reasonable to believe that a shift in metrology from post fabrication sampling to on-line (in-situ) measurement and control is required to achieve more value in the metrology process. This change would require metrology instruments as robust as the processing equipment used in fabrication.