  Contact Hamiltonian dynamics is a subject that has still a short history, but
with relevant applications in many areas: thermodynamics, cosmology, control
theory, and neurogeometry, among others. In recent years there has been a great
effort to study this type of dynamics both in theoretical aspects and in its
potential applications in geometric mechanics and mathematical physics. This
paper is intended to be a review of some of the results that the authors and
their collaborators have recently obtained on the subject.
