We discuss the current status of the proton tensor charge, obtained as the first Mellin moment of the chiral-odd transversity parton distribution extracted from a global analysis of data for inclusive pion-pair production in deep-inelastic scattering and in proton-proton collisions with one transversely polarized proton. We compare this result with other phenomenological extractions and with the direct computation on lattice of the tensor charge as hadronic matrix element of the local chiral-odd tensor operator. The knowledge of the proton tensor charge is important among other things for detecting possible signals of new physics in high-precision low-energy experiments.