Recent Raman data on nanocrystallite arrays are revised within the microscopic theory for Raman peaks positions and broadening (linewidth). The theory combines the elasticity theory-like approach for optical phonons used in order to evaluate the Raman peaks structure and the Green's function method applied for the phonon lines broadening. These theories are supported by the atomistic calculations within the dynamical matrix method for optical phonons and by the bond polarization model used to calculate the Raman intensities. The experimental data on four various nanopowders are analyzed with the use of this theory. The large width of the Raman peak in nanoparticles as compared with the corresponding peak in bulk materials and the width inverse dependence on the particle size previously observed by other researchers are explained within the framework of the theory. It is shown that the theory is capable to extract confidently from the Raman data four important microscopic characteristics of the nanopowder including the mean particle size, the variance of the particle size distribution function, the strength of intrinsic disorder in the particle, and the effective faceting number that parameterizes the particle shape.