Our understanding of the geometry associated with the second Chern class has gradually increased over the last 25 years. It appears in many contexts: it is associated with a 2-dimensional topological field theory and with the Wess-Zumino-Witten model. It plays an essential role in the construction of the String 2-group, and so it has a deep and still imperfectly understood relationship with elliptic cohomology. I’ll give a survey of some ways of thinking about the 2nd Chern class and sketch how some of these approaches are related to each other.