  The concept of Dyall zeroth-order Hamiltonian [Dyall, K. G. J. Chem. Phys.,
102, 4909-4918 (1995)] has been instrumental in the development of intruder-
and parameter-free multireference perturbation theories for the efficient
treatment of static and dynamic correlation in molecular systems. In this
review, we discuss two theoretical approaches based on the Dyall Hamiltonian:
(i) N-electron valence perturbation theory and (ii) multireference algebraic
diagrammatic construction theory. We briefly cover the technical aspects behind
these theories and discuss their relationship. We conclude with a short
description of alternative approaches based on the Dyall Hamiltonian, a
summary, and an outlook on future developments.
