What is consciousness? The best summary I’ve found of where we are up to in understanding this is an article by Susan Blackmore. Susan brings an extra dimension to her understanding – as well as being a psychologist, she is also practises Zen meditation (though she says "I am not a Buddhist", and has experimented with psychedelic drugs.
One perspective she doesn’t mention is Ken Wilber’s Four Quadrants model, in which subjective experience is a different, yet linked, realm to the objective world studied by science. In this model, the sense of self is not reducible to the physical functions of the brain (as most researchers into consciousness in the neuroscience field believe) but they are linked. Makes sense to me.
Most of the information about Wilber’s ideas on the web get very complicated and jargonised very quickly – why I’m not sure. The most accessible description of the basic model is here.