  This is a survey of recent studies of singularity formation in solutions of
spherically symmetric Yang-Mills equations in higher dimensions. The main
attention is focused on five space dimensions because this case exhibits
interesting similarities with Einstein's equations in the physical dimension,
in particular the dynamics at the threshold of singularity formation shares
many features (such as universality, self-similarity, and scaling) with
critical phenomena in gravitational collapse. The borderline case of four space
dimensions is also analyzed and the formation of singularities is shown to be
intimately tied to the existence of the instanton solution.
