Abstract : Modern compilers are responsible for adapting the semantics of source programs into a form that makes efficient use of a highly complex, heterogeneous machine. This adaptation amounts to solve an optimization problem in a huge and unstructured search space, while predicting the performance outcome of complex sequences of program transformations. The polyhedral model of compilation is aimed at these challenges. Its geometrical, non-inductive semantics enables the construction of better-structured optimization problems and precise analytical models. Recent work demonstrated the scalability of the main polyhedral algorithms to real-world programs. Its integration into production compilers is under way, pioneered by the Graphite branch of the GNU Compiler Collection (GCC). Two years after the effective beginning of the project, this paper reports on original questions and innovative solutions that arose during the design and implementation of Graphite.