Higher Gauge Theory is a categorical way of thinking about parallel transport of extended objects. Such parallel transport appears naturally within string and M-theory. In particular, the six-dimensional maximally superconformal theory or at least self-dual strings in four dimensions should be captured by Higher Gauge Theory. I will review some of my recent work in this area, including how M2-brane models fit into the picture, how twistor geometry can yield field equations containing the non-abelian tensor multiplet and give explicit higher versions of the BPST instanton and the 't Hooft-Polyakov monopole. If time permits, I will also talk a bit about a higher version of the IKKT matrix model.