Compact binary systems composed by neutron stars (NS) and black holes (BH) are one of the principal sources of gravitational waves (GW) in the terrestrial interferometers frequency range (10 Hz -1 kHz). In particular NS-BH and NS-NS system merger could be followed by detectable electromagnetic (EM) counterparts, such as short Gamma-Ray Bursts (GRB) and Kilonovae (KNe). The first joint GW and EM observation of a NS-NS coalescence (GW170817) marked the dawn of multi-messenger astronomy era and allowed us to obtain copious information about the merger dynamics, the amount of material ejected, the structure of the outflow and heavy element nucleosynthesis. In this talk, after a brief recall on the merger dynamics, I will describe three different EM counterparts of compact binary mergers, such as short GRBs, KNe and Spindown-powered transients (SDPTs). I will discuss a general method that I developed to reconstruct the lightcurves of transients especially designed for the modelling of electromagnetic counterparts of compact binary mergers, showing a particular application to GRBs. I will also present the preliminary results of my work of hydrodynamic simulations of SDPTs and finally I will briefly discuss how it is possible to infer from a sample of short GRBs a luminosity distribution for KNe.