Quality factor 2.5 X 109 at the wavelength (lambda) equals 0.63 micrometers is reported in approximately 100 micrometers spherical resonators of fused silica with whispering-gallery modes (equivalent finesse F equals 2.5 X 106). Quality-factor 3 X 107 and effective thermal tunability of modes (up to 0.1%) is demonstrated in whispering-gallery microresonators of optical glass. Dispersive bistability and other nonlinear effects are observed at the level of input power about tens of microwatts. Nonlinear properties of optical whispering-gallery modes are investigated by mode cross-modulation technique. Prospects of applications in linear signal processing and quantum-nondemolition measurements are outlined.