Abstract: Levi-flat hypersurfaces are important in the context of minimal sets of holomorphic foliations in complex projective spaces. It is well-known that closed smooth real analytic Levi-flats do not exist in $\mathbb C \mathbb P^n$ for $n>2$, and it is an open problem if such hypersurfaces exist in $\mathbb C \mathbb P^2$. On the other hand, singular real-analytic Levi-flats exist in any dimension, and we discuss some recent developments in this subject.