It's morning here in Europe, departure peak time. We're still flying, but...
The problems mean the takeoff and weight & balance data is missing. It needs to be done manual by each crew. Baggage handling is also manual, so that means counting bags and the cabin crew counting people. Then manually calculating performance data before you can take off.
It's not all of Europe. The airports in Norway are operating as normal. One of the airlines reported booking issues on their website, but I haven't read about any other issues.
Some international flights have been delayed or canceled of course, depending on the route.
KLM was flying, but all flights pass through Schiphol Airport (it's their hub) and Schiphol couldn't board fights for a while. Because of that they ran out of gates for arriving flights, so everyone had to cancel flights to avoid compounding delays. As the biggest user of Schiphol that means KLM had to cancel a lot of flights.
I can't imagine believing that this computation, ordinarily automated by these out of service systems, can be performed correctly by crews that probably haven't had to do this in ... years?
At most places there is an iPad app that does the calculation locally. So it's mostly entering a lot of numbers and checking that the results make sense. Usually both crew members do it individually, and then cross check the results.
For much of their history they were written down or copied on carbon paper and manually processed by phone later. Electronic processing came in the 70s and wasn't universally used until much later. I saw plenty of credit card imprinters in use well into the 90s when I was growing up.