A review is presented of the results obtained in an investigation of the charged particle multiplicity distributions in e$^+$e$^-$ annihilation processes in experiments on the LEP accelerator at CERN. Universality in the energy dependence for the average charged particle multiplicity in e$^+$e$^-$ and p$\pm$p collisions, the KNO scaling for the e$^+$e$^-$ data, the structure in the multiplicity distribution and its relation to the number of jets in an event, the average particle multiplicities in quark and gluon jets, the pattern of ``clans'', and other questions are discussed.