The primordial black holes solution to the dark matter issue has lately received much attention due to the non-detection of dark matter particles (WIMPs or axions) in both direct and indirect channels. These black holes are expected to form at the very beginning of the Universe through the collapse of primordial density fluctuations. Depending on their mass distribution, they can have several observable consequences, thus allowing to set constraints on their density -- and the fraction of dark matter they can represent. The observations range from gravitational micro and femto-lensing to the emission of energetic particles through Hawking radiation. In this seminar, we will focus on the Hawking radiation constraints by extending them from the Schwarzschild primordial black holes (non-rotating) to the Kerr metric (rotating black holes) and from monochromatic mass distributions to extended ones. This work is based on the new public code BlackHawk that computes the Hawking spectra of Schwarzschild/Kerr black holes and that will be briefly presented.