When Lucy's (Scarlett Johanson) boyfriend tricks her into delivering a suitcase to Mr Jang, a Korean gangster, she ends up becoming an unsuspecting drug mule. She's had a package of CPH4 inserted into her abdomen and is tasked with delivering the package to Europe along with 3 others. When Lucy is beaten and kicked by one of the gang members, the package splits and the drugs begin to leak inside her body.
The main storyline focuses around the nootropic substance known as CPH4 which begins to expand Lucy's brain power. As the drug works its way into her cells, she begins to experience new things such as telekinesis abilities, an expanded consciousness, enhanced memory recall and also improved bodily senses.
There are are number of issues in the film such as reliance on the 10% of brain myth and conflating neurological and whole-body enhancement topics with being able to break the laws of physics, accessing information not previously known and telekinetic and time travel abilities.
If one is able to look past these issues, one can see a very strong transhumanist narrative stretching back from the first human, through to a posthuman finale.