  Shape coexistence has been a subject of great interest in nuclear physics for
many decades. In the context of the nuclear shell model, intruder excitations
may give rise to remarkably low-lying excited $0^+$ states associated with
different intrinsic shapes. In heavy open-shell nuclei, the dimension of the
shell-model configuration space that includes such intruder excitations becomes
exceedingly large, thus requiring a drastic truncation scheme. Such a framework
has been provided by the interacting boson model (IBM). In this article we
address the phenomenon of shape coexistence and its relevant spectroscopy from
the point of view of the IBM. A special focus is placed on the method developed
recently which makes use of the link between the IBM and the self-consistent
mean-field approach based on the nuclear energy density functional. The method
is extended to deal with various intruder configurations associated with
different equilibrium shapes. We assess the predictive power of the method and
suggest possible improvements and extensions, by considering illustrative
examples in the neutron-deficient Pb region, where shape coexistence has been
experimentally studied.
