MPI collective communication routines like MPI_Allreduce, MPI_Gather, and MPI_Scatter allow processes in parallel programs to share data. MPI_Allreduce combines data from all processes using a reduction operation like sum or max. MPI_Gather collects portions of a send buffer from each process into a receive buffer. MPI_Scatter distributes different chunks of an array from a root process to other processes. Exercises demonstrate changing data and testing these routines work correctly across processes.