  We consider several variants of SU(3) partial dynamical symmetry in relation
to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such
property is presented in the framework of the interacting boson model (IBM),
including higher order terms, and in its proton-neutron extension (IBM-2). The
cases considered include a single prolate-deformed shape with solvable ground
and $\gamma$ or $\beta$ bands, coexisting prolate-oblate shapes with solvable
ground bands, and aligned axially-deformed proton-neutron shapes with solvable
symmetric ground and $\gamma$ bands and mixed-symmetry scissors and $\gamma$
bands.
