  Lagrangian submanifolds of a Kaehler manifold are called
Hamiltonian-stationary (or $H$-stationary for short) if it is a critical point
of the area functional restricted to compactly supported Hamiltonian
variations. In [B. Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken,
Lagrangian isometric immersions of a real-space-form $M^{n}(c)$ into a
complex-space-form $\tilde{M}^{n}(4c)$, Math. Proc. Cambridge Philo. Soc. 124
(1998), 107-125], an effective method to constructing Lagrangian submanifolds
of constant curvature $\varepsilon$ in complex space form $M^n(4\varepsilon)$
was introduced. In this article we survey recent results on construction of
Hamiltonian-stationary Lagrangian submanifolds in complex space forms using
this method.
