Ask HN: Running SAAS Out of the US and VAT Calculation for Clients in EU?

If I have a SAAS product that runs out of the US but I have clients from the EU region, how do you handle VAT and things ? I mean for example, is the SAAS company responsible to charge/report VAT or is it the client that has to do on their end ? Example: If I have a subscription product for $100/month, I charge the flat rate of $100. Do I need to figure out the VAT and then add on top of this $100 or will the client pay the VAT separately to their authorities in their country ?