Approximating foliations by contact structures

Although their definitions are in some sense opposite, contact structures and foliations display many similarities. This is especially clear in the $3$-dimensional theory of confoliations which unites both structures in a single framework. A famous theorem by Eliashberg and Thurston states that, with a single exception ($\mathbb{S}^1 \times \mathbb{S}^2$ foliated by spheres), any (con)foliation on a $3$-manifold can be approximated by contact structures.