Modelling neutron star interiors in the age of gravitational wave detections

Neutron stars are a fantastic physical laboratory, that allows us to probe fundamental physics, including phenomena such as superfluidity, in regimes that cannot be replicated in terrestrial laboratories. In this talk I will discuss recent advances in theoretical modelling, and show how multi-messenger observations, that make use of both electromagnetic and gravitational wave signals, can be used to constrain fundamental parameters. In particular I will focus on the impact of superfluidity on the theoretical side, and on searches for continuous gravitational waves on the observational side.