String phenomenology is the branch of string theory concerned with making contact with particle physics. The original models involved compactifying ten-dimensional supersymmetric Yang-Mills theory on an internal Calabi-Yau three-fold. In recent years, this picture has been extended to compactifications of supersymmetric Yang-Mills theory in seven, eight or nine dimensions. We review some of this progress and explain the fundamental role played by Higgs bundles in this story.