I will survey the subject starting with examples and the notion of involutivity.
Then we review related topics in generalized Frobenius theorems and the Cartan-Kaehler theory, Finally, we discuss open problems in the following areas:
1) Conservation laws for boundaries and for submanifolds of higher codimensions,
2) Existence of complex varieties (with singularities) in a real hypersurface of a complex space
3) Applications to control theory.