  An isometric immersion $f:M^n\to \tilde M^n$ from a Riemannian $n$-manifold
$M^n$ into a K\"ahler $n$-manifold $\tilde M^n$ is called {\it Lagrangian} if
the complex structure $J$ of the ambient manifold $\tilde M^n$ interchanges
each tangent space of $M^n$ with the corresponding normal space. In this paper,
we completely classify spherical Lagrangian submanifolds in complex Euclidean
spaces. Furthermore, we also provide two corresponding classification theorems
for Lagrangian submanifolds in the complex pseudo-Euclidean spaces with
arbitrary complex index.
