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

Status of the continuous gravitational wave searches in the Advanced Detector Era