This article discusses the formation, magnetic structure, and eruption of solar filaments in terms of two contrasting paradigms. The standard paradigm is that filaments are formed by condensation of plasma on coronal magnetic fields that are twisted or dimpled as a result of photospheric motions. According to this paradigm, filaments erupt when photospheric motions shear the fields, increasing their energy and decreasing their stability. According to a new paradigm, subsurface motions generate toroidal magnetic flux ropes, and after these flux ropes emerge to form active regions, the most twisted parts migrate into the corona to form filaments. Filaments become unstable and are ejected after a sufficient accumulation of twist (i.e., magnetic helicity). Various proposed mechanisms for producing the needed helicity are reviewed, and several observational tests are proposed to differentiate among the possible mechanisms.