Scaling and scale breaking phenomena in QCD jets

The perturbative QCD approach to multiparticle production assuming Local Parton Hadron Duality (LPHD) and some recent results are discussed. Finite asymptotic scaling limits are obtained for various observables, after an appropriate rescaling, in the Double Logarithmic Approximation (DLA). Non-asymptotic corrections are also known in some cases. The DLA applies also to very soft particle production where energy conservation constraints can be neglected. In this region the particle density follows rather well a scaling behaviour over the full energy range explored so far in $e^+e^-$ annihilation