Relationship between the rising movement of the filaments, the evolutions of filament current systems and the flares on 13 May, 1981, 16 May, 1981, and 4 February, 1986, have been studied. We have obtained the following results: (1) The flare-filament current systems show great variety. For the flare of 13 May, 1981, the current system might be considered as a simple current loop. Calculations suggest that it was triggered by tearing-mode spontaneous reconnection caused by the magnetic twist within the filament. The 16 May flare, occurred in the same active region as the 13 May flare, and both eruptions were due to the evolution and the motion of the same filament, but the release of the magnetic energy of the 16 May flare may have taken place in the current sheet beneath the rising filament. This would mean that the flare of 16 May, 1981 result from current-sheet reconnection. Furthermore, the flare of 4 February, 1986 may be the result of the coalescence of two filament current loops. Thus a variety of flares might be explained by different magnetic reconnections caused by different filament rising movements and different filament current systems. (2) The resistive tearing instability could be regarded as the heating mechanism of the preflare phase (for the flare of 4 February, 1986) and sometimes may develop into the hot phase of the flare (for the flare of 13 May, 1981). (3) When we solve the momentum equation, different background fields of the active region should be taken for different active regions. For active region Hale 17644, the potential field can be taken as approximate description of the background field because there is no observed large-scale shear; but for active region 4711, which is strongly stressed, force-free field was chosen to describe the background field. Meantime, calculations show that for the flare of 4 February, 1986, only a force-free field which changes quickly with height could fit the observed rising movement of the filament.