I'm reading Fulton's book. There's an awesome theorem that classifies all smooth toric surfaces as blowups at points starting from either $P^2$ or some Hirzebruch surface.
I want to be more excited about the result rather than the proof, but I don't have intuition to if many surfaces are toric, do we ever meet toric varieties naturally without building them on purpose? It seems rare we'd have a torus action