In most female mammals, including humans, progesterone levels are high during pregnancy, but fall dramatically with labor and childbirth. This fall in progesterone has been shown to play an important role in inducing maternal behavior.
Though progesterone is traditionally thought of as a female hormone, due to its vital role in female reproductive behavior, it plays a significant role in paternal behavior too. Male mice, like many other rodents, tend not to be very good fathers. What little interest they do take in their offspring tends to be marked with aggression. Many male mice attack and even kill their own newborns.
It was thought that this aggression is a result of high testosterone levels, but research now shows that it's actually progesterone that incites these males' aggressive behavior toward their young.
Scientists engineered a strain of mice so that they were immune to progesterone's affects. Not only did these mice show no sign of aggression toward their young, they were actually active in caring for their offspring. So just as a decline in progesterone after childbirth propels maternal behavior, low levels of progesterone in males induces paternal behavior.
These males' aggressive behavior toward other males, however, did not change much. So it seems that while testosterone incites more general aggressive behavior, progesterone incites aggression toward offspring alone. To what extent these findings about the correlations between progesterone levels and paternal behavior are applicable to humans is not clear yet.