Traditionally, condensed matter physicists have classified phases of matter according to their symmetries. Over the last few decades, it became clear that near zero temperature, there are plenty of phases which lie beyond this classification scheme. These intrinsically quantum mechanical states of matter lack any ordinary order parameter; they can be thought of as a strongly fluctuating quantum liquids. Nevertheless, they posses a hidden underlying order, known as "topological order". The quantum Hall effect is a celebrated example of such a phase; several others have been discovered recently, and many more have been predicted theoretically. The elementary excitations of topologically ordered states can be thought of as emergent particles; intriguingly, these particles can obey unu-sual exchange statistics rules which resemble neither those of bosons nor of fermions. This property makes topological phases potentially useful as building blocks for future decoherence-free quantum processing devices. In this talk, I will describe some modern insights into the nature of these phases, and their characterization in term of their quantum entanglement. I will also discuss a new route to realize novel phases that arise on the boundaries of other, previously known topologically ordered states.