What do Pokémon, chemistry, and algebraic geometry have in common? The answer is not just that they are all fun, nor that they all have TV series about them. Rather, they are all concerned with collecting and classifying things! In this talk, I will introduce the idea of classification in algebraic geometry and explain how it can be interpreted depending on what one wants to classify, illustrating this with several examples. Finally, I will briefly describe my own contributions to the classification of Fano fourfolds.