You probably can guess the basic plot just by means of the title and the cover art. A scientist gets teleported with a fly and turns into a fly-human hybrid. What you may not be able to guess is that the film is a one of a kind masterpiece.
This movie is not simply a campy script about a marvel supervillain. It is a psychological-horror trip down the rabbit hole of the fly transformation process. The acting from the 3 main characters is done incredibly well, especially Goldblum. The trick this movie plays on the viewer is that it is not only a horror movie, but at its core a romantic tragedy that explores the power of love with a grotesque creature. The story arc plays out in a fairytale-like fashion similar to Edward Scissor hands or Beauty and the Beast (yet it was made before these movies.)
The first 20 minutes of the movie is non threatening, and focuses on character development which is important for establishing the disturbing elements of the film later to come. The characters have real world flaws and mannerisms that make them convincing and likable. The baboon teleportation failure is the first real messed up moment, and catches the unexpecting viewer off guard.
After Brundle (Goldblum) accidentally teleports with the fly and fuses his genes with it, the transformation into the fly begins. However, it is not instantaneous. The movie focuses on the drawn out psychological madness of the slow transformation process of turning into a monster. At first he experiences euphoria, but this eventually ends and the grotesque reality of the situation takes hold. The fly genes do not just affect him physically, but he has to fight off fly-like instincts as they seep into his brain stronger and stronger as time goes by.
This movie is able to cover deep psychologically horrible themes such as an impending deceased death, or having no next of kin to take your place after death. And having no control of mutating into an evil creature. Be afraid, be very afraid.