How to even begin coding an AI which flies around the player?

Hello,
I am in the process of creating a shooter game in which the enemies will fly close to the player and then fly in curves around the player. I assume a way I could handle this would be with curves that bend around the player like a sphere, but is there a better way to do such a behavior? Thank you!

 

So like a side-scrolling shooter? Yeah, curves would be a very simple and effective way of dealing with this.