The determination of the Cosmic Star Formation Rate Density History is crucial to understand how stellar mass has been assembled in galaxies. I will present the Cosmic SFRD History derived with the VVDS Deep and Ultra-Deep spectroscopic surveys from the global FUV Luminosity Function, in the redshift range 0 < z < 4, i.e. in the past 12 Gyr. I will also describe the global evolution of the dust attenuation within this redshift range. This is the first time that this is done in a coherent manner within a homogeneous galaxy sample across such a broad redshift range. Our results are compelling for models of galaxy formation.