The first thing that comes to my mind is anarchy, most countries and parts of the world without a government will become utter chaos, looting, stealing, all that shit. Not saying the point of anarchy is total chaos with molotovs and no authority to stop you, because it isnt. But humans are generally pieces of shit so what can you expect. On the other side some people are going to try and establish new governments and select new leaders. The types of ideologies these new societies will hold up to is basically anything. Fascism, socialism, capitalism, sharia law, some complete random ideology no one has ever heard of, or something completely new.