  Periodic (almost monochromatic) gravitational waves emitted by rotating,
asymmetric neutron stars are intriguing potential signals in the sensitivity
band of Advanced LIGO and Advanced Virgo detectors. These signals are related
to elastic and magnetic stresses in the neutron-star interior, as well as to
various possible instabilities, and thus are interesting from the point of view
of the largely-unknown neutron star structure. I will describe the main
challenges related to these searches, the current state of the data-analysis
methods and plans for the future.
