The SALT transient follow-up programme began in 2016 and will continue for 5 semesters (until 31 Oct 2018), with an expectation of renewal thereafter. It is currently the only SALT Large Science Programme, and was awarded ~250 ksec. per semester, with a significant fraction (60%) given for the highest priority target-of-opportunity time. The aim is to characterise and study transients across a wide range of classes, currently including (from closest to most distant) cataclysmic variables, novæ and other associated eruptive variables, low- and high-mass X-ray binaries, OGLE and Gaia transients (including tidal disruption events), super-luminous and unusual core-collapse supernovæ, kilonovæ and other candidate optical counterparts to gravitational-wave events, flaring blazars and AGN, and gamma-ray bursts. This programme currently involves four SALT partners, of which South Africa is the major contributor of time (74%) and resources and includes five institutions with over 30 co-investigators. This talk reviewed the nature of the programme and highlighted some of the results to date.