  We present a general review of the projective symmetry group classification
of fermionic quantum spin liquids for lattice models of spin $S=1/2$. We then
introduce a systematic generalization of the approach for symmetric
$\mathbb{Z}_2$ quantum spin liquids to the one of chiral phases (i.e., singlet
states that break time reversal and lattice reflection, but conserve their
product). We apply this framework to classify and discuss possible chiral spin
liquids on triangular and kagome lattices. We give a detailed prescription on
how to construct quadratic spinon Hamiltonians and microscopic wave functions
for each representation class on these lattices. Among the chiral
$\mathbb{Z}_2$ states, we study the subset of U(1) phases variationally in the
antiferromagnetic $J_1$-$J_2$-$J_d$ Heisenberg model on the kagome lattice. We
discuss static spin structure factors and symmetry constraints on the bulk
spectra of these phases.
