Sites using third party shipping apps like ShipIt and Fastway/AP Shipping may be experiencing problems with no shipping rates being loaded at checkout.
If your shipping rates are set up through admin/shipping you are not affected.
We've raised it to Shopify, and they've published a status alert. It looks like it is almost fixed (1pm EST 31 May 2018).
You may be seeing a blank order printer screen when you go in to the app. The good news is that it isn't broken, your browser just needs more permissions.