  Neutron star interiors are a fantastic laboratory for high density physics in
extreme environments. Probing this system with standard electromagnetic
observations is, however, a challenging endeavour, as the radiation tends to be
scattered by the outer layers and the interstellar medium. Gravitational waves,
on the other hand, while challenging to detect, interact weakly with matter and
are likely to carry a clean imprint of the high density interior of the star.
In particular long lived, i.e. `continuous' signals from isolated neutron stars
can carry a signature of deformations, possibly in crystalline exotic layers of
the core, or allow to study modes of oscillation, thus performing gravitational
wave asteroseismology of neutron star interiors. In this article we will review
current theoretical models for continuous gravitational wave emission, and
observational constraints, both electromagnetic and gravitational. Finally we
will discuss future observational possibilities.
