How do people get into new relationship while having feelings for their ex?

I am scared of getting into a relationship with someone that still has feelings for the ex. Anyone feel the same?

I've been reading a lot recently of people that never get over their ex and it scared me. It scared me that in the future I might be in a serious relationship with someone or even marry someone that still deep down has SOME feelings for his ex. And even HE might not know it.
I have never been in a relationship before so I don't know anything about breaking up or getting over someone. How does it work? Do people get into new relationships before they've completely gotten over their previous one? Do people stay in new relationships knowing that they still have some feelings for their ex? Does their new partner know?
Its all just so scary to me. I don't really have a specific question I guess...I just want to understand more.

I guess what scares me the most is some people never get over their exes yet go on to have a family. Isn't that unfair on their new partner? I'm scared of being with someone like that and not even realising it.

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