In my talk, I will present new constraints on light sterile neutrino mixing parameters obtained from both cosmological and direct measurements. For the first time, we model the sterile in a full 3+1 framework coupled to all other neutrino flavours and consistently calculate the cosmological perturbations. Cosmological data dominates the resulting limits on mass splitting and the mixing matrix elements. In addition, we translate the cosmological bounds to the mass parameters directly probed by laboratory searches and obtain the strongest currently available limits. We also find that various hints of eV-scale sterile neutrinos from short-baseline experiments are in severe tension with those cosmological constraints.