We explore the origins of rotational motion in anisotropic fluid theories from the most fundamental perspectives possible: collections of discrete entities or continuous spectra of fluid particles which are allowed to translate and rotate simultaneously. In either case, the starting point of our analysis is the principle of least action applied to rigid body systems involving both translation and rotation. Our methods of analyzing this problem are both very old and very recent, and we hope that the net result of these methods is an injection of much originality into an old problem. Hamiltonian mechanics of a system of discrete particles is considered where explicit accounting is made of both translational and rotational particle motion. The extended Poisson bracket is written down in terms of appropriate generalized coordinates and the Hamiltonian of the system. A similar treatment in terms of quasi-coordinates is also presented. An alternative formulation in terms of two orthogonal unit vectors is offered which simplifies the mathematical description of the system by working in an inertial reference frame with constant, diagonal inertia tensors. This methodology is transferred to a continuum material description in terms of functional relationships and Volterra differentiation. An analogous continuum bracket is derived, and ultimately transferred to a spatial description, along with the Hamiltonian. This results in a derivation of the most general form of the ideal anisotropic fluid equations in terms of the appropriate variables, an important subcase of which is the Leslie-Ericksen theory of liquid crystals. It extends and also provides insight into the molecular origins of the various constitutive relationships of continuum anisotropic fluid theories (such as the inertia tensor, body force, body couple, etc.). Our motivation is to provide, based on the Poisson bracket structure for all different descriptions of rigid particle rotation, an a priori derivation of the Poisson bracket structure corresponding to the rotational motion described in continuum anisotropic fluid theories which also leads to their consistent generalization.