Various strategies and tools for parallelization of Fortran code using multithreading and/or multiprocessing.
Co-arrays: Incorporated into Fortran 2008 and enhanced in Fortran 2015. Available in actively developed compilers from GNU/OpenCoarrays, Cray, and Intel.
MPICH: A flavour of MPI; OpenMPI: another.
OpenMP OMP: multi-platform shared-memory parallel programming in C/C++ and Fortran. This is available for gfortran ( libgomp), and many commercial compilers.
ADAPTOR: Parallel Fortran Compilation System
PGI CUDA Fortran compiler Based on Open64.
PIPS: Automatic Parallelizer and Code Transformation Framework (Fortran to Fortran). A Fortran 95 front end has just been released. There is also a version targetting CUDA (see Par4All).