Since Donaldson-Thomas proposed a programme for studying gauge theory in higher dimensions, there has

been significant interest in understanding special Yang-Mills connections in Ricci-flat 7-manifolds with holonomy

G_2 called G_2-instantons. However, still relatively little is known about these connections, so we begin the

systematic study of G_2-instantons in the SU(2)^2-invariant setting. We provide existence, non-existence and

classification results, and exhibit explicit sequences of G_2-instantons where “bubbling" and "removable

singularity" phenomena occur in the limit. This is joint work with Goncalo Oliveira (Duke).