Recent trends in deep-submicron very large-scale integration (VLSI) circuit technology have resulted in new requirements for algorithms in integrated circuit layout. Much of my work centers on new formulations that capture performance and density criteria in the physical layout phases of computer-aided design (CAD). Our results include near-optimal approximation algorithms for such computationally difficult problems as minimum-cost Steiner tree routing, low-skew clock networks, cost-radius tradeoffs, bounded-density trees, circuit probe testing, high-performing Elmore-based constructions, layout density control, and improved manufacturability.