  We introduce $\Theta$-positivity, a new notion of positivity in real
semisimple Lie groups. The notion of $\Theta$-positivity generalizes at the
same time Lusztig's total positivity in split real Lie groups as well as well
known concepts of positivity in Lie groups of Hermitian type. We show that
there are two other families of Lie groups, SO(p,q) for p<q, and a family of
exceptional Lie groups, which admit a $\Theta$-positive structure. We describe
key aspects of $\Theta$-positivity and make a connection with representations
of surface groups and higher Teichm\"uller theory.
