Future opportunities for gigascale integration (GSI) will be governed by a hierarchy of theoretical and practical limits whose levels can be codified as (1) fundamental, (2) material, (3) device, (4) circuit, and (5) system. Theoretical system limits indicate that in rank order the most serious technological problems impeding progress towards GSI are related to (1) interconnections, (2) heat removal, and (3) transistors. Practical limits on the number of transistors per chip can be extended only if the manufacturing cost per function of GSI continues to decline, which will require, among other advances, enormous progress in semiconductor characterization.