Simulations of lattice gauge theories such as QCD or QED on classical computers have been remarkably successful over the past decades. However, the conventional methods relying on Monte Carlo sampling face limitations in certain regimes, e. g. the notorious sign problem, which is hindering progress in simulating lattice gauge theories at finite chemical potential, theories with topological term, or their real time dynamics. This has motivated the ongoing search for alternative approaches for exploring the dynamics of lattice gauge theories. In this talk, I will discuss recent insights into the dynamics of U(1) lattice  gauge theories, which can be obtained analytically, classically, and from digital quantum simulations.