  In three dimensions, gapped phases can support "fractonic" quasiparticle
excitations, which are either completely immobile or can only move within a
low-dimensional submanifold, a peculiar topological phenomenon going beyond the
conventional framework of topological quantum field theory. In this work we
explore fractonic topological phases using three-dimensional coupled wire
constructions, which have proven to be a successful tool to realize and
characterize topological phases in two dimensions. We find that both gapped and
gapless phases with fractonic excitations can emerge from the models. In the
gapped case, we argue that fractonic excitations are mobile along the wire
direction, but their mobility in the transverse plane is generally reduced. We
show that the excitations in general have infinite-order fusion structure,
distinct from previously known gapped fracton models. Like the 2D coupled wire
constructions, many models exhibit gapless (or even chiral) surface states,
which can be described by infinite-component Luttinger liquids. However, the
universality class of the surface theory strongly depends on the surface
orientation, thus revealing a new type of bulk-boundary correspondence unique
to fracton phases.
