OpenMP and MPI are two common APIs for parallel programming. OpenMP uses a shared memory model where threads have access to shared memory and can synchronize access. It is best for multi-core processors. MPI uses a message passing model where separate processes communicate by exchanging messages. It provides portability and is useful for distributed memory systems. Both have advantages like performance and portability but also disadvantages like difficulty of debugging for MPI. Future work may include improvements to threading support and fault tolerance in MPI.