  Wintgen proved in [P. Wintgen, Sur l'in\'egalit\'e de Chen-Willmore, C. R.
Acad. Sci. Paris, 288 (1979), 993--995] that the Gauss curvature $K$ and the
normal curvature $K^D$ of a surface in the Euclidean 4-space $E^4$ satisfy
$$K+|K^D|\leq H^2,$$ where $H^2$ is the squared mean curvature. A surface $M$
in $\E4$ is called a {Wintgen ideal} surface if it satisfies the equality case
of the inequality identically. Wintgen ideal surfaces in $E^4$ form an
important family of surfaces; namely, surfaces with circular ellipse of
curvature. In this paper, we provide a brief survey on some old and recent
results on Wintgen ideal surfaces and more generally Wintgen ideal submanifolds
in definite and indefinite real space forms.
