I have experience with modern Fortran. The features that make Fortran relevant today are the array operations, simpler memory management than C/C++ (the allocate statement), and the ability to change floating point and integer precision easily. If you are doing math on very large arrays, Fortran is one of the best ways to go. If you are just starting to learn it, try to follow at least the Fortran 2003 standard and up, because it introduces many more modern conveniences. Many people still use Fortran 77 but honestly I see no reason to look at it at all. Fortran 90 really was only the start of the modernization of Fortran. Most compilers (GNU/gfortran and Intel/ifort) already support the Fortran 2003 standard. For a free software solution, stick to GNU (unless you want to pay for the Intel compiler).

Modern Fortran is a bliss, very high level comparable to MATLAB and Python, yet lightening fast, only a professional careful C programmer could get to its speed. Meanwhile, the only high-level programming language that provides a very simple native builtin syntax for one the most difficult types of distributed parallel computing. If you begin to learn Fortran, start from Fortran 2008 and beyond. Most major compilers support all of Fortran 2008 and and most of Fortran 2018, including Intel Fortran, NAG, GNU, Fujitsu, Cray, PGI, ...