Exploring the Past
An inevitable part of getting to know a partner is talking about past relationships.
Unless the couple is very young, both will have had relationships. But when there is a marriage involved, this conversation about the past can take on a more serious tone. A key question will be why the marriage broke up. But this is a serious issue, and it should not be forced. However, a reluctance to open up at all about the marriage could be a warning sign.
If the divorce is recent, the man is likely to be still emotionally fragile, and more than likely to not really be ready to get involved in a new relationship.
His reasons for dating may be dubious, from wanting to be seen to be "moving on" to replacing his wife. It is always wise to be cautious when dating a newly divorced man.
Many women struggle with a man's existing responsibilities.
The obvious important responsibility that a divorced man may have is to his children. A woman dating a divorced man must exercise great tact and understanding when children are involved. She should not rush into a "stepmother" role, but neither should she resent the time that he spends with his children, if this is reasonable. It is possible for the situation to resolve itself in a constructive and happy way, but it requires good will on everybody's part.