Cosmology faces a pressing challenge with the Hubble constant (H0β)
tension, where the locally measured rate of the Universe's expansion does not
align with predictions from the cosmic microwave background (CMB) calibrated
with ΞCDM model. Simultaneously, there is a growing tension involving
the weighted amplitude of matter fluctuations, known as S8,0β tension.
Resolving both tensions within one framework would boost confidence in any one
particular model. In this work, we analyse constraints in f(T) gravity, a
framework that shows promise in shedding light on cosmic evolution. We
thoroughly examine prominent f(T) gravity models using a combination of data
sources, including Pantheon+ (SN), cosmic chronometers (CC), baryonic acoustic
oscillations (BAO) and redshift space distortion (RSD) data. We use these
models to derive a spectrum of H0β and S8,0β values, aiming to gauge
their ability to provide insights into, and potentially address, the challenges
posed by the H0β and S8,0β tensions