If one of the parts is outside the EU, things get more complicated. This is a reason why some work as freelancers/contractors. It simplifies things. The company

If one of the parts is outside the EU, things get more complicated. This is a reason why some work as freelancers/contractors. It simplifies things. The company may offer some help with the bureaucracy, but the people I know all have ended using a local third-party service to manage all that, anyway. Also, consider something else. Many companies, even if they are outside the EU, may already have an EU-based subsidiary. Once they have that, contracting in all the EU will go through that and simplify things a lot since it will effectively be a contract within the EU again. This is the case for a couple of friends I know. I can't tell you anything for the case where the employee is the one outside the EU, sorry.