  We discuss the different signals, in gravitational and electromagnetic waves,
emitted during the merger of two compact stars. We will focus in particular on
the possible contraints that those signals can provide on the equation of state
of dense matter. Indeed, the stiffness of the equation of state and the
particle composition of the merging compact stars, strongly affect e.g. the
life time of the post-merger remnant and its gravitational wave signal, the
emission of the short gamma-ray-burst, the amount of ejected mass and the
related kilonova. The first detection of gravitational waves from the merger of
two compact stars in August 2017, GW170817, and the subsequent detections of
its electromagnetic counterparts, GRB170817A and AT2017gfo, is the first
example of the era of "multi-messenger astronomy": we discuss what we have
learned from this detection on the equation of state of compact stars and we
provide a tentative interpretation of this event, within the two families
scenario, as due to the merger of a hadronic star with a quark star.
