The review is devoted to a new branch in magnetic resonance spectroscopy based on the optical detection of stochastic spin precession: laser spin noise spectroscopy (SNS). The SNS method, like EPR spectroscopy, makes it possible to study the energy structure of the magnetic states of the medium but does not imply excitation of regular spin precession and, due to the use of a laser-polarimetric signal detection channel, has a number of unique properties. In the review, we consider the specific information capabilities of the magnetic resonance noise technique and describe experiments demonstrating the efficiency of this approach for studying the energy-related and dynamic properties of spin subsystems in solid and gaseous paramagnets. Via the example of exciton-polariton condensate emission, we consider the specific features of polarization noise in secondary emission, including the case of unpolarized light. A rigorous theoretical description of the polarimetric spin noise signal formation is given based on the model of inelastic (Raman) light scattering by elementary angular momentum carriers.