Wurtzite Boron Nitride ($w$BN) is a wide band gap BN polymorph with peculiar mechanical properties (hardness and stiffness). After its first synthesis in 1963 as a transformation of hexagonal BN ($h$BN) under high temperature and pressure conditions, a lot of progress have been made in order to stabilize wurtzite phase at atmospheric pressure. Today the crystallization of good quality samples is finally possible. This fact motivates our first principles study of the electronic, vibrational and light absorption and emission properties of $w$BN over a wide range of pressures. Our findings are important in view of the potential use of $w$BN as a dielectric for integration in BN-based technologies in optoelectronics and harsh environment applications.