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Specs
Pros
Pro Fortran libraries are still at the core of scientific computing
Julia libraries are Fortran.
Python libraries are partially implemented in Fortran.
Matlab libraries are fortran.
Cuda C++ libraries are wrap ups to Fortran libraries.
Pro Maximum performance
Fortran was designed from the beginning for maximum performance, and as one of the oldest languages in continuous use, the compilers are now very mature. Even hand-optimized assembly is usually slower, because the compilers are that smart.
Pro Top performance in fields of Computational Biology and Computational Physics
Computational natural sciences are a top interest in the up and coming scientific milestones specially in Genetics and Electromagnetism.
Pro The language has refused to die
And it is because all of a sudden C++ won't do it and Fortran would prevent in expending dozens of millions of dollars in new infrastructure.
Cons
Con Use in computational physics was only due to timing, and is rapidly changing
On Cray systems and other supercomputers Fortran was the language used for research due to implementation, not performance. At this point giant supercomputers have been almost completely replaced with massively distributed systems that Fortran cannot very well take advantage of.
Con Most existing uses are on ancient systems
While this may be good for now, eventually these jobs will disappear.
Con Most modern bioinformatics has long since gone to more flexible languages
Despite hits to performance, nearly all modern research is done using languages like python which are much, much faster to prototype on and can be optimised using their massive library of carefully optimised libraries in native (often assembly) code. The result is faster iteration, more useful results in shorter time and more portable code that can be reused for later projects.
Con Requires archaic costly and brittle architectural design
Fortran is principally deigned for applications to be precisely purpose built and optimised by empirically solving a specified case. As a result, solutions are not portable or adaptable at all, especially after the hand crafting necessary for performance on Big Iron.
Con Expensive work force
Ultra experienced Fortran developers charge small fortunes and they need teams of developers that charge as high to fix projects.
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