  Beyond black holes and neutron stars, new hypothetical compact objects have
been proposed as potential astrophysical entities. In general, their properties
have not yet been fully explored or understood, nor has it been proven whether
or not they exist in nature. They are the so-called $\textit{exotic compact
objects}$, theoretical equilibrium configurations in the strong regime of
gravity that involve new exotic physical phenomena deeply related to
fundamental questions of theoretical physics (e.g., the nature of dark matter,
the formation of singularities, or the presence of horizons). Among these
exotic objects, there are those that require the existence of new fields and
particles beyond the Standard Model, such as boson stars and ultralight bosons;
those that seek to describe the dense equation of state of neutron stars as an
even more extreme state of matter made up of free quarks; or those that exhibit
additional properties related to extensions of General Relativity or even
quantum gravity. However, in order to move from theoretical objects to
astrophysical objects, their dynamics and stability must first be assessed by
performing numerical-relativity simulations under the premise that solutions
that are unstable on dynamical timescales will never completely form, being, at
most, a transient state that will not be able to play any astrophysical role.
Furthermore, numerical simulations also make it possible to extract the
gravitational radiation from relevant astrophysical scenarios, such as the
collapse of exotic stars or binary mergers, which could then be compared with
current and upcoming LIGO-Virgo-KAGRA gravitational-wave detections.
