  Strongly interacting arrays of Rydberg atoms provide versatile platforms for
exploring exotic many-body phases and dynamics of correlated quantum systems.
Motivated by recent experimental advances, we show that the combination of
Rydberg interactions and appropriate lattice geometries naturally leads to
emergent $\mathbb{Z}_2$ gauge theories endowed with matter fields. Based on
this mapping, we describe how Rydberg platforms could realize two distinct
classes of topological $\mathbb{Z}_2$ quantum spin liquids, which differ in
their patterns of translational symmetry fractionalization. We also discuss the
natures of the fractionalized excitations of these $\mathbb{Z}_2$ spin liquid
states using both fermionic and bosonic parton theories, and illustrate their
rich interplay with proximate solid phases.
