  An immersion $\phi \colon M \to \tilde M$ of a manifold $M$ into an
indefinite Kaehler manifold $\tilde M$ is called purely real if the almost
complex structure $J$ on $\tilde M$ carries the tangent bundle of $M$ into a
transversal bundle. In this article we survey some recent results on purely
real surfaces in Kaehler surfaces as well as on Lorentz surfaces in Lorentzian
Kaehler surfaces.
