With submillimeter size and optical Q up to similar to 10(10), microspheres with whispering-gallery (WG) modes are attractive new component for fiber-optics/photonics applications and a potential core in ultra-compact high-spectral-purity optical and microwave oscillators. In addition to earlier demonstrated optical locking of diode laser to WG mode in a microsphere, we report on microsphere application in the microwave optoelectronic oscillator, OEO. In OEO, a steady-state microwave modulation of optical carrier is obtained in a closed loop including electro-optical modulator, fiber-optic delay, detector and microwave amplifier. OEO demonstrates exceptionally low phase noise (-140 dBc/Hz at 10kHz from similar to 10GHz carrier) with a fiber length similar to 2km. Current technology allows to put all parts of the OEO, except the fiber, on the same chip. Microspheres, with their demonstrated Q equivalent to a kilometer fiber storage, can replace fiber delays in a truly integrated device. We have obtained microwave oscillation in microsphere-based OEO at 5 to 18 GHz, with 1310nm and 1550nm optical carrier, in two configurations: 1)with external DFB pump laser, and 2)with a ring laser including microsphere and a fiber optic amplifier. Also reported is a simple and efficient fiber coupler for microspheres facilitating their integration with existing fiber optics devices.