In this talk some examples of local Raman studies of molecules adsorbed on various catalysts and metal electrodes will be presented. First, examples of standard Raman microscopic measurements with spatial resolution of about one micrometer will be shown. In many experiments we are, however, able to record spectrum dominated by the contribution from molecules adsorbed on the area significantly smaller than the area actually illuminated by the laser beam. Such measurements are possible, for example, on surfaces covered with the metal nano-resonators. Theoretical calculations of the efficiency of Raman scattering for molecules adsorbed at the system of metal nano-resonators showed that the efficiency of Raman scattering for molecules adsorbed at so-called "hot spots" can be even ten orders of magnitude higher than the efficiency of Raman scattering for molecules adsorbed at "cold zones". Extremely large Raman enhancements are accomplished with a rather high spatial confinement. Therefore, although there is a very large number of adsorbed molecules in the focal area of the Raman microscope (about one square micrometer), in many cases it is possible to measure Raman spectrum dominated by the contribution from only a few semi-randomly chosen molecules (clusters). Some practical applications of "a few molecules" surface-enhanced Raman scattering (SERS) measurements will be presented. The mechanism of very large efficiency of Raman scattering for some molecules (clusters) will be also analysed. In the last part of the talk the combination of Raman spectroscopy and scanning probe microscopy (STM or AFM) - so called tip-enhanced Raman spectroscopy (TERS) - will be described. In this technique only the Raman scattering of the molecules which are very close to the tip is enhanced. Therefore, TERS has both very large spectroscopic and spatial sensitivity.