Compact stars are the most exotic and challenging laboratories in the Universe to test the properties of baryonic matter. Inside these objects ultracold matter is known to be in the most extreme conditions characterized by very high baryonic densities, rotation speeds and strong magnetic fields. Understanding the complex physical phenomena occurring inside such compact astrophysical objects as neutron stars, hybrid stars, and quark stars requires a profound knowledge of a wide range of scientific disciplines in physics, as well as an analysis of a large amount of observational and experimental data. I will describe how combination of data coming from nucleus-nucleus collision experiments, astrophysical observations, gravitational wave signal coming from the first NS-NS binary merger open a unique new window to study the properties of matter inside the compact stars and phase transition from hadron matter to quark-gluon plasma in their core.
