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The spectrum of the cosmic microwave background (CMB) is known to be extremely close to a perfect blackbody. However, even within standard cosmology several processes occurring in the early Universe lead to distortions of the CMB at a level that might become observable in the future. This could open an exciting new window to early Universe physics. In my talk I will then explain in more detail why the cooling of matter in the early Universe causes a negative mu- and y-type distortion and how the damping of primordial small-scale perturbations before recombination could allow placing interesting constraints on different inflationary models.