  In this paper we review some connections recently discovered between
topological insulators and certain classes of quantum spin liquids, focusing on
two and three spatial dimensions. In two dimensions we show the integer quantum
Hall effect plays a key role in relating topological insulators and chiral spin
liquids described by fermionic excitations, and we describe a procedure for
"generating" a certain class of topological states. In three dimensions we
discuss interesting relationships between certain quantum spin liquids and
interacting "exotic" variants of topological insulators. We focus attention on
better understanding interactions in topological insulators, and the phases
nearby in parameter space that might result from moderate to strong
interactions in the presence of strong spin-orbit coupling. We stress that
oxides with heavy transition metal ions, which often host a competition between
electron interactions and spin-orbit coupling, are an excellent place to search
for unusual topological phenomena and other unconventional phases.
