Matter in the interior of neutron stars can reach densities several times larger than that of atomic nuclei. Properties of matter at such high densities can be constrained from astrophysical observations and gravitational wave signals produced by binary mergers. However, we lack a first principles description that will help us to understand better the state of matter at the core of the stars. Gauge/gravity duality has proven to be useful to extract qualitative lessons about the quark-gluon plasma produced in heavy ion collisions, and similar lessons may be awaiting for dense cold matter. I will review the recent progress on this approach and possible future directions.