This paper surveys some recent developments in the application of combinatorial optimization to VLSI design. We focus on integer programs arising in wire routing and PLA partitioning. Typically, the integer programs we are interested in are computationally difficult. We present approaches to approximately solving them by rounding the solutions to the relaxed linear programs. The resulting algorithms run in polynomial time and have provable performance guarantees. We also introduce the notion of multiterminal multicommodity flows, and point out their relevance to VLSI routing. © 1992.