The recent first observing run with Advanced LIGO has made gravitational waves accessible as a unique new tool for astronomy and fundamental physics. One of the major scientific prospects for gravitational wave observations of merging neutron star binaries is to measure the equation of state of ultra-dense nuclear matter. The successful extraction of this information from the signal requires robust theoretical models describing the imprint of neutron star matter on the waveforms. During the binary’s gradual inspiral, the matter effects in the waveform arise from tidal interactions. The dominant signature is due to adiabatic tides and characterised by the neutron stars’ tidal deformability or Love number parameters. In addition, dynamic tides related to the neutron stars’ fundamental oscillation modes also start to appreciably influence the signal. I will describe these effects and their inclusion in the Effective-One-Body approach for modelling waveforms. This model further includes the merger signal in the case of neutron star – black hole binaries where the neutron star may get tidally disrupted. I will show comparisons with the results from numerical relativity simulations and outline open issues for future work.