Invention of the scanning force microscope in 1986 and development of micro and nanofabrication technologies yielded a new generation of vibration based miniature sensors of physical, chemical and biological parameters, with sensitivity which could not be achieved before. This promoted again the research of micro and nanoelectromechanical systems (MEMS and NEMS) in the fields that have been dominated by semiconductor electronics for more than a half of century.In this paper the principles of operation of the miniature vibrating structures are given. A particular attention is given to the fact that the mass of these structures is of the order of tens of picograms, and that their dimensions can be in the submicrometer range, where the effects of Brownian motion of particles in the surroundings become significant. These effects are expressed as thermomechanical noise which in most cases determines the ultimate sensor performances. Also, adsorption and desorption (AD) of particles (atoms, molecules) on the surface of miniature vibrating structures generate the AD noise.Vibrating micro-and nanostructures are important not only for the new sensor components, but also for a multitude of other applications. As an illustration, I will mention a new generation of MEMS oscillators, which successfully replaces the traditional quartz oscillators in some contemporary applications. Also, a new generation of processors which utilize built-in miniature mechanical structures is envisioned.