  The famous Nash embedding theorem published in 1956 was aiming for the
opportunity to use extrinsic help in the study of (intrinsic) Riemannian
geometry, if Riemannian manifolds could be regarded as Riemannian submanifolds.
However, this hope had not been materialized yet according to \cite{G}. The
main reason for this was the lack of control of the extrinsic properties of the
submanifolds by the known intrinsic invariants. In order to overcome such
difficulties as well as to provide answers to an open question on minimal
immersions, the first author introduced in the early 1990's new types of
Riemannian invariants, his so-called $\delta$-curvatures, different in nature
from the "classical" Ricci and scalar curvatures. The purpose of this article
is to present some old and recent results concerning $\delta$-invariants for
Lagrangian submanifolds of complex space forms.
