  Extracting the unique information on ultradense nuclear matter from the
gravitational waves emitted by merging, neutron-star binaries requires robust
theoretical models of the signal. We develop a novel effective-one-body
waveform model that includes, for the first time, dynamic (instead of only
adiabatic) tides of the neutron star, as well as the merger signal for
neutron-star--black-hole binaries. We demonstrate the importance of the dynamic
tides by comparing our model against new numerical-relativity simulations of
nonspinning neutron-star--black-hole binaries spanning more than 24
gravitational-wave cycles, and to other existing numerical simulations for
double neutron-star systems. Furthermore, we derive an effective description
that makes explicit the dependence of matter effects on two key parameters:
tidal deformability and fundamental oscillation frequency.
