The polyhedral model for loop parallelization has proved to be an effective tool for advanced optimization and automatic parallelization of programs in higher-level languages. Yet, to integrate such optimizations seamlessly into production compilers, they must be performed on the compiler's internal, low-level, intermediate representation (IR). With Polly, we present an infrastructure for polyhedral optimizations on such an IR. We describe the detection of program parts amenable to a polyhedral optimization (so-called static control parts), their translation to a Z-polyhedral representation, optimizations on this representation and the generation of optimized IR code. Furthermore, we define an interface for connecting external optimizers and present a novel way of using the parallelism they introduce to generate SIMD and OpenMP code. To evaluate Polly, we compile the PolyBench 2.0 benchmarks fully automatically with PLuTo as external optimizer and parallelizer. We can report on significant speedups.