An interesting and helpful essay on the theories of strong and weak emergence that have taken on a certain cachet among philosophers and scientists in recent years can be found at Science and Theology News.
The more interesting of the two is strong emergentism which, briefly put, is the view that there are laws which produce increasing complexity in the world and that complex systems are not explicable simply in terms of their component parts:
Among those who think about emergence, said Australian philosopher David J. Chalmers, two main positions have developed: strong emergence and weak emergence. Supporters of weak emergence make the claim that the more fundamental theory can in principle explain the phenomena of the higher-level theory. And many also argue that emergent laws and properties, even if they do exist, don't cause anything on a lower level of reality to change in any way.
According to this view, mind, for example would be an epiphenomenon of the material brain and if we knew how the material substrate worked in all of its detail we'd understand exactly what mind is.
Those who favor strong emergence, meanwhile, search for examples of emergence where the emergent property, or alleged law, cannot be reduced in this way. To use a common emergentist phrase, the whole really is greater than the sum of the parts - and the whole really causes things to happen among lower-level parts. "In the broadest sense, as elements combine into complex structures, new properties emerge that are surprising and not present in earlier, simpler stages, that new things come about through the appearance of complex structures," said William Hasker, an emeritus professor of philosophy at Huntington University in Huntington, Ind. "As such, these new things are not added from the outside but through the complex structure itself."
In this view, mind is not reducible simply to chemical reactions in the brain. It is a higher order phenomenon that actually affects the lower order phenomena of the brain which in turn exerts control obver the even lower order phenomena of the physical body. In strong emergent thinking there is a hierarchy to nature and no level in the hierarchy is completely reducible to lower levels.
Supporters of weak emergence say that stronger forms leave the door open to an unwarranted intrusion of religion into science, even though many atheists also believe in strong emergence.
Indeed, it does leave the door open, and it looks as if the more we learn about the natural world the harder it will be to keep that door shut.
Update: See this interview for more on the emergent paradigm.