The second LIGO-Virgo observing run (O2) enabled the exciting multi-messenger discovery of GW170817 with gravitational waves emitted from the inspiral and merger of two neutron stars and the electromagnetic emission from the ejected matter such as gamma-ray bursts and kilonovae. In particularly, AT2017gfo, the so-called kilonova has been clearly seen for the first time in the optical and near infrared. The kilonova is produced by the radioactive decay of r-process elements, synthesized in neutron-rich ejecta matter, ejected during the merger. In this talk, we will present the observational challenges to detect and characterize the kilonovae. We will also present the additional benefit for the study of the astrophysics of these sources, as it is a complement to the GW and GRB signals. In particular, we will focus on multi-messenger studies of the equation of state of supra-nuclear matter in BNS mergers that help to constrain astrophysical scenarios.