  This overview focuses on the notion of partial dynamical symmetry (PDS), for
which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but
is not shared by the Hamiltonian. General algorithms are presented to identify
interactions, of a given order, with such intermediate-symmetry structure.
Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the
framework of models based on spectrum generating algebras. PDSs of various
types are shown to be relevant to nuclear spectroscopy, quantum phase
transitions and systems with mixed chaotic and regular dynamics.
