There have been great improvements in medical technology in the last few centuries, which has led to very significant increases in life expectancy. Yet, while medical technology has stopped the vast majority of us dying young, it has not been very effective at increasing the maximum age that humans can live to. Ramesses II lived to the age of 90, even though the life expectancy in ancient Egypt might have been below 30. Similarly, the English aristocracy between 1500-1550 already had a life expectancy of 71, meaning that quite a few of them will have lived into their 80s. The oldest person the world, as of the writing of this question, is aged 117. It is unclear whether anybody in the ancient world lived to a similar age (there were many claims of extreme age and very poor record keeping), but it certainly does not seem completely impossible.
Recently, though, there have been attempts to actually extend he upper limit of human lifespan. The Methuselah Foundation has managed to keep mice alive for the equivalent of 180 human years. Yet, it is unclear whether this achievement will be transferrable to humans.
As of June 2018, several people have reached milestones in human lifespans:
46 people have reached the age of 115.
19 people have reached the age of 116.
9 people have reached the age of 117.
2 people have lived beyond the age of 117.
Only one person is verified to have lived to 120, and they lived to 122.