  We introduce the notion of the $\textit{Nevanlinna pair}$ for a pair $(X,
D)$, where $X$ is a projective variety and $D$ is an effective Cartier divisor
on $X$. This notion links and unifies the Nevanlinna theory, the complex
hyperbolicity (Brody and Kobayashi hyperbolicity), the big Picard type
extension theorem (more generally the Borel hyperbolicity), as well as the
algebraic hyperbolicity. The key is to use the Nevanlinna theory on parabolic
Riemann surfaces recently developed by P\v{a}un and Sibony.
