Macroscopic systems composed of particles whose time evolution is governed by the rigid body dynamics are called rigid body fluids. Such fluids could be, for example, macromolecular fluids composed of rigid macromolecules. Kinetic theory and hydrodynamics of these systems are introduced by using the method of Hamiltonian modeling. The physical basis of this method is the requirement that solutions to the governing equations agree with results of the experimental observations that constitute the empirical basis of equilibrium thermodynamics. The advantages of the Hamiltonian method are best displayed on the level of extended hydrodynamics, i.e., hydrodynamics with state variables composed of classical hydrodynamics fields and some extra fields characterizing the rigid body motion of the particles. Both the time evolution equations and the formula for the extra stress tensor are obtained without the need of closure approximations. Moreover, the formula for the extra stress tensor is guaranteed to be compatible with the rest of the time evolution equations. Qualitative properties of solutions of the governing equations derived in the paper lead to the conclusion that rigid body fluids possess a nonsymmetric stress tensor and exhibit elastic behavior. Both of these features have been seen in simulations.