Abstract: Spin characterizes how particle states re-phase under changes of frame that leave their momentum and energy invariant. But all familiar field theories propagate particles that transform trivially under some of these transformations --- in particular, those that involve boosts. For example, until very recently it was not known how to describe the four-dimensional "continuous spin'' particles (CSPs) in field theory. In this talk, I will introduce a new covariant, local action for gauge fields, whose physical excitation in four dimensions is a CSP. The theory is simply formulated as a gauge theory in a "vector superspace", but can also be formulated in terms of a tower of symmetric tensor gauge fields. In the limit of vanishing spin-scale ρ, the theory smoothly recovers familiar gauge-theory actions. The theory readily generalizes to higher or lower dimensions; in 2+1 dimensions, the only kind of massless particle with non-trivial physical spin is CSP-like. These "panyons" can be understood as massless generalizations of anyons, but are simpler in key respects.