  We present in this article a survey of recent results in value distribution
theory for the Gauss maps of several classes of immersed surfaces in space
forms, for example, minimal surfaces in Euclidean $n$-space ($n$=3 or 4),
improper affine spheres in the affine 3-space and flat surfaces in hyperbolic
3-space. In particular, we elucidate the geometric background of their results.
