Petascale parallel computers with more than a million processing cores are expected to be available in a couple of years. Although MPI is the dominant programming interface today for large-scale systems that at the highest end already have close to 300,000 processors, a challenging question to both researchers and users is whether MPI will scale to processor and core counts in the millions. In this paper, we examine the issue of scalability of MPI to very large systems. We first examine the MPI specification itself and discuss areas with scalability concerns and how they can be overcome. We then investigate issues that an MPI implementation must address in order to be scalable. To illustrate the issues, we ran a number of simple experiments to measure MPI memory consumption at scale up to 131,072 processes, or 80%, of the IBM Blue Gene/P system at Argonne National Laboratory. Based on the results, we identified nonscalable aspects of the MPI implementation and found ways to tune it...