  Quantum simulation is at the heart of the ongoing "second" quantum
revolution, with various synthetic quantum matter platforms realizing evermore
exotic condensed matter and particle physics phenomena at high levels of
precision and control. The implementation of gauge theories on modern quantum
simulators is especially appealing due to three main reasons: (i) it offers a
new probe of high-energy physics on low-energy tabletop devices, (ii) it allows
exploring condensed matter phenomena that are prominent in gauge theories even
without a direct connection to high-energy physics, and (iii) it serves as a
banner of experimental benchmarking given the plethora of local constraints
arising from the gauge symmetry that need to be programmed and controlled. In
order to faithfully model gauge-theory phenomena on a quantum simulator,
stabilizing the underlying gauge symmetry is essential. In this brief review,
we outline recently developed experimentally feasible methods introduced by us
that have shown, in numerical and experimental benchmarks, reliable
stabilization of quantum-simulator implementations of gauge theories. We
explain the mechanism behind these \textit{linear gauge protection} schemes,
and illustrate their power in protecting salient features such as gauge
invariance, disorder-free localization, quantum many-body scars, and other
phenomena of topical interest. We then discuss their application in experiments
based on Rydberg atoms, superconducting qubits, and in particular ultracold
neutral atoms in optical superlattices. We hope this review will illustrate
some facets of the exciting progress in stabilization of gauge symmetry and in
gauge-theory quantum simulation in general.
