The U.S. and China really got the censorship ball rolling, and there are countless others just itching to cleanse the internet of content they find disagreeable.
The scary thing is what might happen if companies who are forced to censor their content become unwilling or actually unable to censor the content to the extent required by whatever domestic law. In that case, we wouldn't even need some sort of overarching international law to "control" the internet because the most restrictive law any given nation puts in place will be the controlling law. This has already happened in all manners of international law, where a given country, often the US, has the most restrictive law that all other countries and therefore de facto obligated to follow.