Rick Deckard AKA Blade Runner (Harrison Ford) is tasked to track down and "retire" (a euphemism for kill) 4 replicants (aka Bio-cyborgs) who have escaped from off-world colonies and returned to the Earth. The replicants are genetic inventions created by Tyrell Corporation, made in order to colonise and work on other "Off World" planets.
The replicants are only given a 4 year life span and it is believed that the 4 replicants who have returned to Earth may be there to try to find a way extend their longevity.
Deckard is first tasked by Tyrell to test his assistant Rachel, a replicant with implanted memories that Tyrell says are used to give the replicants an emotional buffer. Rachel takes much longer for Deckard to test as replicant than usual and Tyrell says that is because she is designed to be "more than human".
Deckard sets off after testing Rachel to track down the 4 replicants. The first one is found working at a cabaret bar of some kind. Blade Runner tests her and she attacks him and flees the scene. Deckard scurries to his feet and goes after the replicant. After a chase, Deckard has the replicant in his sights and he shoots her twice, leaving her dead. This is witnessed by one of the other replicants.
There are multiple Transhumanist elements to the movie, the replicants themselves are examples of bio-augmentation, cloning, simulated consciousness, implanted memories (Rachel, and perhaps Blade Runner), and genetic enhancements with one of the characters referring to himself as a "genetic designer".
The replicants are also extreme examples of longevity advocacy, given that they only have a 4 year life span.