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The chapter provides a brief overview of shaping and measuring techniques of the vortex spectra (squared amplitudes and initial phases of vortex modes) including radial indices. The main physical mechanisms causing the formation of laser beams with a complex vortex composition, in particular, in biological media, are indicated, and the need for a digital analysis of vortex spectra is substantiated. It is the analysis of vortex spectra that allows us to find the orbital angular momentum and informational entropy (Shannon’s entropy) of perturbed laser beams in real time. In the main part of the chapter, we consider in detail a new approach for measuring vortex spectra without cuts and gluing of the wavefront, based on digital analyzing high-order intensity moments of complex beams and sorting the vortex beam in computer memory sells. It is shown that certain types of weak local inhomogeneities cause a vortex avalanche causing a sharp dips and bursts of the orbital angular momentum spectra and quick ups and downs of the informational entropy. An important object of analysis is also the vortex spectra of beams scattered by simple opaque obstacles such as a hole, a disk, and a sector aperture.