Cosmology is currently in a crisis known as the Hubble tension, the observation that redshift increases with distance about 10% faster than expected in the ΛCDM standard cosmological paradigm with parameters calibrated to fit the CMB anisotropies. A promising explanation for this is that we live near the centre of a large local underdensity or void. This is suggested by observations of source number counts across the whole electromagnetic spectrum, with near-infrared results implying that the density is about 20% below average out to 300 Mpc across 90% of the sky and most of the galaxy luminosity function (ApJ, 775, 62). Outflows from this KBC void can induce enough extra redshift to plausibly solve the Hubble tension (MNRAS, 499, 2845). I will discuss various tests of this proposal. At low redshift, the bulk flow of galaxies traces the average velocity of matter within a sphere centred on our location. The observed bulk flow curve is in good agreement with the void model predictions (MNRAS, 527, 4388). Looking further out, it is possible to infer the H0 parameter from data in a narrow redshift range centred on z. Such an empirical H0(z) curve agrees quite well with expectations in the void model, which predicts a return to the CMB-derived H0 beyond the void (MNRAS, 536, 3232). This result is related to recently submitted work on baryon acoustic oscillations (BAOs), which show a deviation from ΛCDM expectations (Arxiv:2501.17934). I will explain how the BAO observables would be affected by a local void. I will then present BAO results compiled over the last twenty years. These results fit better if the local void is included, thanks to good agreement with ΛCDM at high redshift but a persistent anomaly at lower redshift.