Motivated by the discrepancy in measurements of H0 between local and global probes, we investigate whether teleparallel gravities could be a better model to describe the present-day observations or at least to alleviate the H0 tension. Specifically, in this work we study and place constraints on three popular f(T) models in light of the Planck-2018 cosmic microwave background data release. We find that the f(T) power-law model can alleviate the H0 tension from 4.4σ to 1.9σ level, while the f(T) model of two exponentials fails to resolve this inconsistency. Moreover, for the first time, we obtain constraints on the effective number of relativistic species Neff and on the sum of the neutrino masses Σmν in f(T) gravity. We find that the constraints obtained are looser than in ΛCDM. However, the introduction of massive neutrinos into the cosmological model alleviates the H0 tension for the power-law model. Finally, we find that whether a viable f(T) theory can mitigate the H0 tension depends on the mathematical structure of the distortion factor y(z,b). These results could provide a clue for theoreticians to write a more physical-motivated expression of f(T) function.