Lots of places will not give notifications to applicants until after the job posting closes and all the applications have been screened. Some places are very, very, very slow. For me it's not uncommon to be extended an interview 4, 5, 6 weeks after I submitted the application. I once had one place call me something like 3 months after! (and suprisingly this was a private company and not a governmental department)

When you're not hearing back, you sometimes need to get in touch with the company and remind them about your application. Sometimes HR loses your paperwork, sometimes the recruitment gets put on hold, sometimes HR forgets that the company was taking applications and sometimes the job posting is fake because HR is doing market research.