Some of the most surprising phenomena concerning contact geometry in dimension three are associated with Seifert fibered spaces. In particular, Ko Honda and I have found Seifert fibered spaces that admit no tight contact structures and ones that admit "tight but not fillable" contact structures. In this talk, I will first explain what the prior sentence means and why the examples mentioned therein are surprising. I will then discuss a general procedure for studying contact structures on Seifert fibered spaces, and indicate how the above examples can be understood from this procedure.