摘要： In the year 1970, Kobayashi introduced an intrinsic canonical metric for every complex manifold $X$, and when this obtained metric is everywhere non-degenerated, $X$ is said to be complex hyperbolic. He conjectured that, in all dimensions, most manifolds should be complex hyperbolic. In this talk we shall present the history and some recent developments in this subject, including the Green-Griffiths-Lang conjecture.