We use 3 years of data from the Swift/BAT survey to select a complete sample of X-ray blazars above 15 keV. This sample comprises 26 Flat-Spectrum Radio Quasars (FSRQs) and 12 BL Lac objects detected over a redshift range of 0.03<z<4.0. We use this sample to determine, for the first time in the 15--55 keV band, the evolution of blazars. We find that, contrary to the Seyfert-like AGNs detected by BAT, the population of blazars shows strong positive evolution. This evolution is comparable to the evolution of luminous optical QSOs and luminous X-ray selected AGNs. We also find evidence for an epoch-dependence of the evolution as determined previously for radio-quiet AGNs. We interpret both these findings as a strong link between accretion and jet activity. In our sample, the FSRQs evolve strongly, while our best-fit shows that BL Lacs might not evolve at all. The blazar population accounts for 10-20 % (depending on the evolution of the BL Lacs) of the Cosmic X-ray background (CXB) in the 15--55 keV band. We find that FSRQs can explain the entire CXB emission for energies above 500 keV solving the mystery of the generation of the MeV background. The evolution of luminous FSRQs shows a peak in redshift (zc=4.3±0.5) which is larger than the one observed in QSOs and X-ray selected AGNs. We argue that FSRQs can be used as tracers of massive elliptical galaxies in the early Universe.FONDAPFONDAP