VLSI design is probably the most fascinating application area of combinatorial optimization. Virtually all classical combinatorial optimization problems, and many new ones, occur naturally as subtasks. Due to the rapid technological development and major theoretical advances the mathematics of VLSI design has changed significantly over the last ten to twenty years. This survey paper gives an up-to-date account on the key problems in layout and timing closure. It also presents the main mathematical ideas used in a set of algorithms called BonnTools, which are used to design many of the most complex integrated circuits in industry.