Barnard's Star exhibits the highest known proper motion (1° per 351 years), a phenomenon attributed to its close proximity (less than 6 light-years) and a substantial radial velocity of 110 km/s ...
Astronomers have long been able to measure the movement of stars in our 'line of sight' (i.e. the movement towards or away from us) by measuring the redshift, which is caused by the Doppler effect.