From the abstract: we study foliations on CR manifolds and show the following. (1). For a strictly pseudoconvex CR manifold \(M\), the relationship between a foliation \(F\) on \(M\) and its pullback \(\pi^*F\) to the total space \(C(M)\) of the canonical circle bundle of \(M\) is given, with emphasis on their interrelation with the Webster metric on \(M\) and the Fefferman metric on \(C(M)\), respectively. (2). With a tangential CR foliation \(F\) on a nondegenerate CR manifold \(M\), we associate the basic Kohn-Rossi cohomology of \((M,F)\) and prove that it gives the basis of the \(E_2\) term of the spectral sequence naturally associated to \(F\). (3). For a strictly pseudoconvex domain \(\Omega\) in a complex Euclidean space and a foliation \(F\) defined by the level sets of the defining function of \(\Omega\) on a neighborhood \(U\) of \(\partial\Omega\), we give a new axiomatic description of the Graham-Lee connection, a linear connection on \(U\) which induces the Tanaka-Webster connection on each leaf of \(F\). (4). For a foliation \(F\) on a nondegenerate CR manifold \(M\), we build a pseudo-Hermitian analogue to the theory of the second fundamental form of a foliation on a Riemannian manifold, and apply it to the flows obtained by integrating infinitesimal pseudo-Hermitian transformations on \(M\).