Powerful flares from blazars with minute-timescale variability are challenging for current emission models. An excellent candidate for describing such events is relativistic magnetic reconnection, a process that transfers energy from magnetic fields to non-thermal particles contained in compact regions, denoted as plasmoids. Recent particle-in-cell simulations have been able to fully capture the dynamical properties of the plasmoids, such as their acceleration and growth. In this talk, I will show that the plasmoids of magnetic reconnection in blazar jets can produce powerful flares whose temporal and spectral properties are consistent with the observations. Multiple flares with a range of flux-doubling time-scales (minutes to several hours) and luminosities are expected during a reconnection event that may last several days or even longer.