Taut foliations are closely related to the concept of Reebless foliation. A taut foliation cannot have a Reeb component, since the component would act like a "dead-end" from which a transverse curve could never escape; consequently, the boundary torus of the Reeb component has no transverse circle puncturing it. A Reebless foliation can fail to be taut but the only leaves of the foliation with no puncturing transverse circle must be compact, and in particular, homeomorphic to a torus.

The existence of a taut foliation implies various useful properties about a closed 3-manifold. For example, a closed, orientable 3-manifold, which admits a taut foliation with no sphere leaf, must be irreducible, covered by ${\displaystyle \mathbb {R} ^{3}}$ , and have negatively curved fundamental group.

By a theorem of Hansklaus Rummler and Dennis Sullivan, the following conditions are equivalent for transversely orientable codimension one foliations ${\displaystyle \left(M,{\mathcal {F}}\right)}$  of closed, orientable, smooth manifolds M:^{[2][1]: 158}

• ${\displaystyle {\mathcal {F}}}$  is taut;
• there is a flow transverse to ${\displaystyle {\mathcal {F}}}$  which preserves some volume form on M;
• there is a Riemannian metric on M for which the leaves of ${\displaystyle {\mathcal {F}}}$  are least area surfaces.