  We classify and characterize three dimensional $U(1)$ quantum spin liquids
(deconfined $U(1)$ gauge theories) with global symmetries. These spin liquids
have an emergent gapless photon and emergent electric/magnetic excitations
(which we assume are gapped). We first discuss in great detail the case with
time reversal and $SO(3)$ spin rotational symmetries. We find there are 15
distinct such quantum spin liquids based on the properties of bulk excitations.
We show how to interpret them as gauged symmetry-protected topological states
(SPTs). Some of these states possess fractional response to an external $SO(3)$
gauge field, due to which we dub them "fractional topological paramagnets". We
identify 11 other anomalous states that can be grouped into 3 anomaly classes.
The classification is further refined by weakly coupling these quantum spin
liquids to bosonic Symmetry Protected Topological (SPT) phases with the same
symmetry. This refinement does not modify the bulk excitation structure but
modifies universal surface properties. Taking this refinement into account, we
find there are 168 distinct such $U(1)$ quantum spin liquids. After this
warm-up we provide a general framework to classify symmetry enriched $U(1)$
quantum spin liquids for a large class of symmetries. As a more complex
example, we discuss $U(1)$ quantum spin liquids with time reversal and $Z_2$
symmetries in detail. Based on the properties of the bulk excitations, we find
there are 38 distinct such spin liquids that are anomaly-free. There are also
37 anomalous $U(1)$ quantum spin liquids with this symmetry. Finally, we
briefly discuss the classification of $U(1)$ quantum spin liquids enriched by
some other symmetries.
