There is a type of filament that forms closed contours encircling regions of one polarity of magnetic field, while the surrounding region has the opposite polarity. One distribution of ring-filaments has sizes 2R = 40,000 to 160,000 km with the maximum around 100,000 km; the other distribution (with filaments and filament channels) has bigger sizes, with a maximum around 300,000 km. At low and mid latitudes the radial component Brs (radial for the Sun) in the region outlined by filaments varies from 50 to 100 gauss, while the longitudinal component Bϕ, varies from 10 to 30 gauss. The total current inside the filament is 1010 – 1011 A, the ratio R/a ≈ 5 to 10, the magnetic flux crossing the surface is ≈ 1021 – 1022Mx; the magnetic energy is ≈ 1029 – 1031erg. Polar ring-filaments at latitudes 60° – 80° are related to the polar magnetic field reversal and the quasi-flare processes at the poles during the field reversal. Correlation between Brs and Bϕ, for the polar filament bands cannot be satisfactorily explained. A theoretical model using the conservation laws is used to study the relations between the various fields, currents, etc. of shrinking polar ring-filaments and their evolution. According to this theory ring-filaments should rise higher above the photosphere when shrinking. However, observations show that the height lowers. Presumably the discrepancy is due to the lack of dissipation in the model.