  We introduce the notion of intertwined quantum phase transitions (IQPTs), for
which a crossing of two configurations coexists with a pronounced
shape-evolution of each configuration. A detailed analysis in the framework of
the interacting boson model with configuration mixing, provides evidence for
this scenario in the Zr isotopes. The latter exhibit a normal configuration
which remains spherical along the chain, but exchanges roles with an intruder
configuration, which undergoes first a spherical to prolate-deformed
[U(5)$\to$SU(3)] QPT and then a crossover to $\gamma$-unstable
[SU(3)$\to$SO(6)].
