Multi-site move to new server question.

As I don't know how this works, I thought I'd better ask the question.

I have a multi-site network with multiple sub-domains. I am about to move it from a shared server to a VPS. Am I going to have any issues with the sub-domains?

When I move the network to the VPS, are the sub-domains still going to work?

I can't afford to get this wrong, so your advice is appreciated.

Best regards,