Philosophers of mind wonder if mental properties can be reduced to neural states. For instance, is it possible to reduce my perception of redness to a particular brain state? The answer to these questions is not simple, but some potential approaches that could be taken are:
1) Supervenience theory which has been given the label "property dualism." It posits that there are not two substances (body and soul) but two kinds of properties (mental and physical attributes) which stand in some kind of dependent relationship that preserves their distinctness but coequal real status.
2) Eliminative materialism (EM) which entails completely reducing mental states to brain states (usually in an ontological sense). But one downside to EM is that it wants to do away with talk of emotions and subjective states (qualia or raw feels), thereby replacing them with neuroscientific terminology.
3) Biological naturalism which is John Searle's take on the philosophy of mind says that all conscious states arise from lower-level brain processes. So consciousness is then a higher-level brain process that arises from neuronal activity.
Reductionism is not always wrong, but one problem is that it normally oversimplifies complex phenomena. Josef Seifert wrote an overlooked book about getting back to the things themselves (based on a saying by Edmund Husserl). In that work, Seifert demonstrates why reductionism could be problematic. The bottom line is that many think the reduction of subjectivity to synaptic connections and neural firings is overly simplistic, but I personally am inclined to favor this kind of reductionism. I am a Christian materialist, so I have to reconcile physicalism as it pertains to humans with my belief in God. Yet I see no genuine conflict between these two ideas.