Pulsars are simple electromagnetic machines that operate in extreme physical conditions. Pulsars are powered by the rotation of magnetic fields of order 108 - 1013 Gauss that mediate the conversion of their rotational energy into MHD winds and at the same time accelerate particles to energies sufficiently high to produce GeV (or even TeV) photons. The last decade the plethora of observational data mainly from Fermi-LAT revolutionized the study and the understanding of the pulsar high-energy emission. I will discuss pulsar magnetosphere models emphasizing the beneficial interaction between theory and observations. I will present the recently discovered fundamental plane of gamma-ray pulsars and I will show 3D macroscopic and self-consistent kinetic PIC models that provide a solid interpretation of a broad spectrum of the observations. Our models uncover relations between fundamental macroscopic and microscopic parameters providing a deep understanding of the physical mechanisms behind the observed high-energy emission. This makes this class of astrophysical objects a model example that can be used as a starting point for the study of other systems (e.g., black-holes, merging neutron stars), which actually have many features similar to those found in pulsars.