  In these proceedings we summarise how the determinantal structure for the
conditional overlaps among left and right eigenvectors emerges in the complex
Ginibre ensemble at finite matrix size. An emphasis is put on the underlying
structure of orthogonal polynomials in the complex plane and its analogy to the
determinantal structure of $k$-point complex eigenvalue correlation functions.
The off-diagonal overlap is shown to follow from the diagonal overlap
conditioned on $k\geq2$ complex eigenvalues. As a new result we present the
local bulk scaling limit of the conditional overlaps away from the origin. It
is shown to agree with the limit at the origin and is thus universal within
this ensemble.
