Higher-dimensional gauge theories from string theory

We review some recent developments regarding supersymmetric field theories in six and five dimensions. In particular, we will describe the classification of supersymmetric six-dimensional theories with a holographic IIA dual; they are "linear quivers" consisting of chains of many SU (or SO/Sp) gauge groups connected by hypermultiplets and tensor multiplets. We will also describe the wider classification of supersymmetric six-dimensional theories that can be engineered in F-theory; these are also chains, but they include exceptional gauge groups and copies of a more exotic "E-string" theory with a single tensor and E8 flavor symmetry. Finally we discuss some properties of these theories under compactification to lower dimensions.