  Gravity can be formulated as a gauge theory by combining symmetry principles
and geometrical methods in a consistent mathematical framework. The gauge
approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime
geometries, providing the adequate formalism for metric-affine theories of
gravity with curvature, torsion and non-metricity. In this paper, we analyze
the structure of gauge theories of gravity and consider the relation between
fundamental geometrical objects and symmetry principles as well as different
spacetime paradigms. Special attention is given to Poincar\'{e} gauge theories
of gravity, their field equations and Noether conserved currents, which are the
sources of gravity. We then discuss several topics of the gauge approach to
gravitational phenomena, namely, quadratic Poincar\'{e} gauge models,
the~Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of
general relativity, quadratic metric-affine Lagrangians, non-Lorentzian
connections, and the breaking of Lorentz invariance in the presence of
non-metricity. We also highlight the probing of post-Riemannian geometries with
test matter. Finally, we briefly discuss some perspectives regarding the role
of both geometrical methods and symmetry principles towards unified field
theories and a new spacetime paradigm, motivated from the gauge approach to
gravity.
