Pulsar magnetospheres are often considered as ideal astrophysical sites for particle acceleration in relativistic pair plasmas. The particle-in-cell (PIC) technique is well-suited to study both the evolution of the fields and particle acceleration from first principles. I will present a series of global PIC simulations of both aligned and misaligned pulsars. The results clearly support that the current sheet is an efficient accelerator of particles, and possibly the source of energetic radiation in pulsars. I will discuss these results in the context of young gamma-ray pulsars.