I discuss the influence of electromagnetic and weak dipole moments on spin-spin correlations in the tau pairs produced in electron-positron, quark-antiquark and photon-photon processes. Such processes have been observed in the proton-proton and peripheral heavy-ion collisions at the LHC. Extensions of the Standard Model amplitudes, including the tau anomalous magnetic and electric dipole moments, are implemented in the TauSpinner MC program. This also allows us to test a possible phase-shift between vector and axial-vector couplings of the Z boson to tau leptons. Relation between New Physics contributions to dipole moments and the Standard Model EFT is briefly addressed. A few examples of observables sensitive to the tau-tau spin correlations and dipole moments will be presented.