  The Hamiltonian structures of several hybrid kinetic-fluid models are
identified explicitly, upon considering collisionless Vlasov dynamics for the
hot particles interacting with a bulk fluid. After presenting different
pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the
paper extends the treatment to account for a fluid plasma interacting with an
energetic ion species. Both current-coupling and pressure-coupling MHD schemes
are treated extensively. In particular, pressure-coupling schemes are shown to
require a transport-like term in the Vlasov kinetic equation, in order for the
Hamiltonian structure to be preserved. The last part of the paper is devoted to
studying the more general case of an energetic ion species interacting with a
neutralizing electron background (hybrid Hall-MHD). Circulation laws and
Casimir functionals are presented explicitly in each case.
