Classical chaos can be found in vector fields with a phase space of dimension at least three. Are there even more complicated types of chaos in higher dimensions? The answer is yes, as was shown recently by the construction of a five-dimensional Lorenz-type system; one also speaks of wild chaos. I will discuss how wild chaos arises via bifurcations of an associated noninvertible map of the punctured plane, which contains the complex quadratic family as a special case.