Simulations, ODEs, tight for-loops seem to be high on the lists.
“Generic” data science doesn’t, or indeed general, unscientific programming.
Perhaps this is not right, or outdated, but my impression is that Julia is perhaps very well suited to _some_ scientific programming, not necessarily all of it, despite the broad statements.
Julia is a general-purpose programming language, despite having roots in scientific programming. Its performance characteristics with its high latency and runtime memory overhead makes it unsuitable for a number of non-scientific applications. But not all. I think Julia would work excellent as a webserver backend, for example.
I mostly use it for DNA sequence processing, which is not really numerical programming, but more string processing. There it shines. I wouldn't want to make a video game in Julia or fly a plane using Julia software.
The bang-for-your-buck of adding Numba to existing Python code is why we passed on Julia. Give it a try.
My dream python is pypy+mypy+numba. Alas, pypy doesn't play nice with the others "(