We describe the extraction of the transversity distribution for the first time based on the global analysis of pion-pair production in deep-inelastic scattering and in proton-proton collisions with one transversely polarized proton. The extraction involves di-hadron fragmentation functions, which are taken from the analysis of the corresponding pion-pair production in electron-positron annihilation. We discuss the impact of COMPASS pseudodata from a future measurement of deep-inelastic scattering on transversely polarized deuterons. The knowledge of transversity is important among other things for detecting possible signals of new physics in high-precision low-energy experiments.