Recent work on hyperbolic spaces (Q1365431)

This is a survey article on the recent and not so recent results on Kobayashi hyperbolic complex spaces. It covers among the other topic the construction of hyperbolic hypersurfaces in projective space (particularly for small dimensions), hyperbolicity of complements to hyperplanes, finiteness results for integral points over functional fields (so diophantine problems along the Lang conjecture). There are several interesting remarks on the problem of algebraic characterization of hyperbolicity and the definition of hyperbolicity over non-archimedean fields.