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Abstract We review a recent progress of a superconductivity and a charge Kondo effect mediated by valence skippers which are elements skipping the valence state. To understand the valence skipping phenomenon, we introduce a negative-U effect phenomenologically, and we show an origin of the negative-U effect, a superconductivity and charge Kondo effect based on the negative-U effect. We also show a new mechanism in which the valence skipping phenomenon and charge Kondo effect are understood unifiedly by the pair hopping interaction. As an experimental progress, we review a charge Kondo effect and a superconductivity discovered in Tl-doped PbTe. Especially, we focus on a drastic increase of the inverse of the relaxation time (1/T 1) observed around the Kondo temperature by the nuclear magnetic resonance experiment, and we suggest a possible theoretical scenario on the basis of the effective model with the pair hopping interaction. Finally, we discuss the related materials, and describe the perspective of valence skipping phenomenon.