Solar prominences and filaments (prominences projected against the solar disk) exhibit a large variety of fine structures which are well observed down to the resolution limit of ground-based telescopes. We describe the morphological aspects of these fine structures which basically depend on the type of a prominence (quiescent or active-region). Then we review current theoretical scenarios which are aimed at explaining the nature of these structures. In particular we discuss in detail the relative roles of magnetic pressure and gas pressure (i.e., the value of the plasma-beta), as well as the dynamical aspects of the fine structures. Special attention is paid to recent numerical simulations which include a complex magnetic topology, energy balance (heating and cooling processes), as well as the multidimensional radiative transfer. Finally, we also show how new ground-based and space observations can reveal various physical aspects of the fine structures including their prominence-corona transition regions in relation to the orientation of the magnetic field.
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