Although the luminosity growth for Tevatron Run II was significantly slower than expected, steady growth of luminosity has been demonstrated during last three years with the peak luminosity of 1.02×1032 cm-2s-1 achieved in July 2004. Suppression of instabilities has been a valuable contributor to the luminosity growth. The report discusses the transverse instabilities in Tevatron and Recycler and their suppression by feedback systems. Although Tevatron bunch-by-bunch transverse damper was initially designed to suppress only the dipole mode, in reality, the damper effectively suppresses some head-tail modes. The reason of such suppression and ways to improve it are also discussed.