For a semisimple complex Lie group $G$ and its real form $G_0$, we have finitely many $G_0$-orbits in a $G$-flag manifold. An open $G_0$-orbit is called a flag domain. For example, Hermitian symmetric domains or period domains are flag domains. In this talk, I will talk about cycle-connectivity and pseudoconcavity of flag domains and show our recent result.