The Thylacine (Thylacinus cynocephalus) also known as the Tasmanian Tiger, or Marsupial Wolf is believed to have gone into extinction in 1936 when the last known specimen died at Hobart Zoo, Australia. Competition with dingoes, and bounties paid to hunters (in order to protect farmed sheep) are cited as likely causes.
Since then there have been hundreds of plausible reports of sightings but none has yet been scientifically verified.
In March 2017, the Centre for Tropical Environmental and Sustainability Science (TESS) at James Cook University, Australia, began a research project using 50 high-tech ‘camera traps’ which will monitor possible Thylacine activity on Cape York Peninsula in Far North Queensland.
Press release and full details here
A 2016 paper in the journal Global Change Biology points out that “Each year, two or three species that had been considered to be extinct are rediscovered.”
Other researchers, however, are less optimistic “ […] our results suggest that attempts to rediscover the thylacine will likely be unsuccessful.” source.