The kagome lattice provides a fascinating playground to study geometrical frustration, topology and strong correlations. The newly discovered kagome metals AV$_3$Sb$_5$ (A=K, Rb, Cs) exhibit various interesting phenomena including topological band structure and superconductivity. Nevertheless, the nature of the symmetry breaking in the CDW phase is not yet clear, despite the fact that it is crucial to understand whether the superconductivity is unconventional. In this work, we perform scanning birefringence microscopy and find that six-fold rotation symmetry is broken at the onset of the CDW transition temperature in all three compounds. Spatial imaging and angle dependence of the birefringence show a universal three nematic domains that are 120$^\circ$ to each other. We propose staggered CDW orders with a relative $\pi$ phase shift between layers as a possibility to explain the three-state nematicity in AV$_3$Sb$_5$. We also perform magneto-optical Kerr effect and circular dichroism measurements on all three compounds, and the onset of the both signals is at the CDW transition temperature, indicating broken time-reversal symmetry and the existence of the long-sought loop currents in the CDW phase. Our work strongly constrains the nature of the CDWs and sheds light on possible unconventional superconductivity in AV$_3$Sb$_5$.