  After discussing the limitations inherent to all set-theoretic reflection
principles akin to those studied by A. L\'evy et. al. in the 1960's, we
introduce new principles of reflection based on the general notion of
\emph{Structural Reflection} and argue that they are in strong agreement with
the conception of reflection implicit in Cantor's original idea of the
unknowability of the \emph{Absolute}, which was subsequently developed in the
works of Ackermann, L\'evy, G\"odel, Reinhardt, and others. We then present a
comprehensive survey of results showing that different forms of the new
principles of Structural Reflection are equivalent to well-known large
cardinals axioms covering all regions of the large-cardinal hierarchy, thereby
justifying the naturalness of the latter.
