Blazars are jetted active Galactic Nuclei with the jet axis oriented close to the line of sight of the observer. Non-thermal emission processes in the jet cover the whole electromagnetic spectrum from radio wavelengths to TeV gamma rays, with a characteristic double-humped Spectral Energy Distribution (SED). Relativistic amplification effects on the observed fluxes make their jets ideal candidates for detection at any wavelength. A physically motivated “blazar sequence” has been proposed years ago, although is still heavily disputed as being due to observational selection biases. The sequence relates bolometric power to peak frequencies and luminosities of the two-humped Spectral Energy Distribution of blazars: the frequencies shift to higher energies ,and luminosities dim, along with decreasing power of the sources. At the low end of the luminosity range a subclass of blazars with extreme properties lies, so far poorly populated given that it eludes the best survey of the gamma-ray sky that is currently available, the one built over the data from the Fermi/LAT satellite. Nevertheless these extreme blazars are of the utmost scientific interest, standing at the crossroads of high energy astrophysics of the sources, astro-particle physics, cosmology and fundamental physics.