Who will take care of children in the 21st century now that both parents are more and more likely to have full-time jobs? The old solution was to more-or-less force women take care of them (this is not saying that many women would not want to). But eventually women figured out that this is a bit unfair. And it is very unlikely that men in general would like to be put into the position that women were in (and in some ways still are).

Here are a few ideas about what may happen:
1- Children of working parents get handed over to professional nannies or day care centers. Sounds pretty scary, in fact even Brave New World-ish.
2- Parents work from home and take care of kids at the same time. Perhaps this would be feasible in the future for some professions, but it is not yet likely to happen on any large scale. (Note many companies still preferring employees without families.)
3- Grandparents/Extended family takes care of children. This may just be the best general solution for now. Another problem is the increasingly large percentage of the population that is retired. Grandparents who are willing to do this would be saved boredom and (in some cases) the feeling of uselessness that comes with increasing age, and parents would be able to trust them a lot more than they can trust someone they hired from an ad.

Will it happen? Who knows. It's very likely that the future will be a combination of the three. I just hope that whatever kind of child-rearing becomes dominant, it does not consist of leaving the kids in front of the TV all day.