Integrated circuits with backside power delivery capabilities are provided. An integrated circuit may include a substrate having front and back surfaces, a first interconnect stack formed on the front surface, and a second interconnect stack formed on the back surface. Routing structures that carry data signals, control signals, and other user signals may be formed only in the first interconnect stack. A large majority of routing structures that carry power supply signals may be formed in the second interconnect stack. Decoupling capacitor circuitry such as deep trench capacitors may be formed in the back surface of the substrate. The integrated circuit may be mounted on a package substrate. The first interconnect stack may be coupled to the package substrate via wire bond pads, whereas the second interconnect stack may be coupled to the package substrate via an array of solder bumps.