The cohomology of a variety is a sequence of vector spaces that captures the global structure of the variety, and it can be used to study various aspects of the variety, such as its connectivity, its Betti numbers, and its intersection theory." This is what GPT says, but what it doesn't say is how the cohomology of a variety is a mysterious object that is more than just a sequence of vector spaces. In this talk, I will give a gentle overview of the development that took place in the past 100 years, which paints an intricate but only partially complete picture.