Most polygamy in the western world nowadays appears to be 'serial polygamy', in which a man has a series of wives, with children from each wife. Usually the wives are divorced, though sometimes it is through death.
Sometimes the woman has a series of husbands, and children from each, though this does not appear to occur as often as the man having a series of wives.
Some sectors also have men with more than one wife concurrently, usually in the form of a 'first wife' and a side 'girlfriend', both of whom may have children.
It is even more rare for a woman to have several concurrent men in their lives. Those are usually called prostitutes, and they may have several children by some of those men.
In olden times, and also in the Muslim world, a man would legally have multiple wives (up to four in the Muslim religion, I believe). Some religious sects in the western world do also allow for such polygamy (offshoots of the Mormon church, for example).