  Spiral spin liquids are unique classical spin liquids that occur in many
frustrated spin systems, but do not comprise a new phase of matter. Owing to
extensive classical ground-state degeneracy, the spins in a spiral spin liquid
thermally fluctuate cooperatively from a collection of spiral configurations at
low temperatures. These spiral propagation wavevectors form a continuous
manifold in reciprocal space, \textit{i.e.}, a spiral contour or a spiral
surface, that strongly governs the low-temperature thermal fluctuations and
magnetic physics. In this paper, the relevant spin models conveying the spiral
spin liquid physics are systematically explored and the geometric origin of the
spiral manifold is clarified in the model construction. The spiral spin liquids
based on the dimension and the codimension of the spiral manifold are further
clarified. For each class, the physical properties are studied both generally
and for specific examples. The results are relevant to a wide range of
frustrated magnets. A survey of materials is given and future experiments are
suggested.
