EU Member states (now Austria; France is checking) have now started to copy, the not really well drafted, German Hate Speech Act (NetzDG). The laws provide for wide  take down obligations (also beyond hate speech and other severe infringements) and processes as well as requirements to appoint local representatives. The applicability of these laws to international networks cannot always be (easily) determined. 

Read more in our article and hope a more reasonable and practical Act will come on EU level soon.