The interplay of spin-orbit coupling and correlations opens a new 
playground to study a variety of effects ranging from helical
Luttinger liquids to quantum spin systems generated by threading 
pi-fluxes through correlated topological insulators. In this talk, 
I will concentrate on the Kane-Mele model supplemented by a Hubbard 
U. After discussing the salient features of the non-interacting 
model - topological invariants and edge states - I will concentrate
on the above mentioned correlations driven effects. The results 
obtained are based on large scale quantum Monte Carlo simulations 
which turn out to be free of the infamous sign problem for this 
specific class of models.