  Gauge theories of conformal spacetime symmetries are presented which merge
features of Yang-Mills theory and general relativity in a new way. The models
are local but nonpolynomial in the gauge fields, with a nonpolynomial structure
that can be elegantly written in terms of a metric (or vielbein) composed of
the gauge fields. General relativity itself emerges from the construction as a
gauge theory of spacetime translations. The role of the models within a general
classification of consistent interactions of gauge fields is discussed as well.
