  The report presents an exhaustive review of the recent attempt to overcome
the difficulties that standard quantum mechanics meets in accounting for the
measurement (or macro-objectification) problem, an attempt based on the
consideration of nonlinear and stochastic modifications of the Schroedinger
equation. The proposed new dynamics is characterized by the feature of not
contradicting any known fact about microsystems and of accounting, on the basis
of a unique, universal dynamical principle, for wavepacket reduction and for
the classical behavior of macroscopic systems. We recall the motivations for
the new approach and we briefly review the other proposals to circumvent the
above mentioned difficulties which appeared in the literature. In this way we
make clear the conceptual and historical context characterizing the new
approach. After having reviewed the mathematical techniques (stochastic
differential calculus) which are essential for the rigorous and precise
formulation of the new dynamics, we discuss in great detail its implications
and we stress its relevant conceptual achievements. The new proposal requires
also to work out an appropriate interpretation; a procedure which leads us to a
reconsideration of many important issues about the conceptual status of
theories based on a genuinely Hilbert space description of natural processes.
We also discuss the possibility and the problems one meets in trying to develop
an analogous formalism for the relativistic case. Finally we discuss the
experimental implications of the new dynamics for various physical processes
which should allow, in principle, to test it against quantum mechanics.
