  A projective variety $X\subset\mathbb{P}^N$ is $h$-identifiable if the
generic element in its $h$-secant variety uniquely determines $h$ points on
$X$. In this paper we propose an entirely new approach to study
identifiability, connecting it to the notion of secant defect. In this way we
are able to improve all known bounds on identifiability. In particular we give
optimal bounds for some Segre and Segre-Veronese varieties and provide the
first identifiability statements for Grassmann varieties.
