On the geometry of higher-spin gauge fields

We review a recent construction of the free-field equations for totally symmetric tensors and tensor-spinors that exhibits the corresponding linearized geometry. These equations are not local for all spins >2, involve unconstrained fields and gauge parameters, rest on the curvatures introduced long ago by de Wit and Freedman and reduce to the local (Fang)Fronsdal form upon partial gauge fixing. We also describe how the higherspin geometry is realized in free string field theory, and how the gauge fixing to the light cone can be effected.