I think its fair to say that it shines for numerical computation, but you can perform other tasks with Julia with ease.

For example, the idea of writing some number-crunching as a webservice with MATLAB or Octave is not an option, but with Julia is totally possible (and has been done more than once already) - and it builds on strong foundations (e.g. libuv). Heres an example (disclaimer: my own site) http://iaindunning.com/2013/sudoku-as-a-service.html