There are no concerns for me (Alhamdulillah) as my wife's past I know as she has been very strict in keeping distance from na-mehram males before our marriage. My past, she doesn't need to know, as most of my friends were right when they said no sane woman would ever like to have any kind of relationship with me. I am very lucky to get a sane and wise woman (MashaAllah) who accepted me as her future husband (which also might not have been possible if her parents had not advised her to do so).
Even if she had a past of relationships, I won't have cared about it unless she brought it again and again during our conversations by living in the past, at the cost of the time that should be used for concentrating on our relationship in the present
I would like to share a humble opinion regarding people who change girl friends / boy friends from time to time only for fun. Let us consider our heart (emotions and love) to be like a piece of paper. Let us divide this paper into as many pieces as many people we have been deeply involved with, and write the name of each person on his respective piece of paper. The deeper our relationship was with a person, the bigger size of piece s/he gets. Now after cutting pieces from the original paper and distributing them to the respective people, the remaining portion of the paper left with us is actually the amount of love / emotions we have saved for the person we are going to marry in life. So the less we get involved (deeply) with people the more we are able to save ourselves (our emotions and love) for our future life partner. Because, no matter how much we try, it wont be easy to totally remove those people from our mind and heart and focus "only" on our life partner. So, I personally think it is better to develop and proceed a relationship ONLY when we are serious to consider that person as a potential life partner (without letting the person play with our emotions and exceed the physical limits) instead of passing the time for fun.
I might be totally wrong, as I don't have any authentic source to support my argument, but this is how I sincerely feel. Allah knows BEST! May Allah (s.w.t) bless us with the wisdom to make the right decisions in life and put "barakah" in our relationships