The review exposes basic concepts and manifestations of the singular and structured light fields. The presentation is based on deep intrinsic relations between the singularities and the rotational phenomena in light; it involves essentially the dynamical aspects of light fields and their interactions with matter. Due to their topological nature, the singularities of each separate parameter (phase, polarization, energy flow, etc.) form coherent interrelated systems (singular networks), and the meaningful interconnections between the different singular networks are analysed. The main features of singular-light structures are introduced via generic examples of the optical vortex and circular vortex beams. The review describes approaches for generation and diagnostics of different singular networks and underlines the role of singularities in formation of optical field structures. The mechanical action of structured light fields on material objects is discussed on the base of the spin-orbital (canonical) decomposition of electromagnetic momentum, expressing the special roles of the spin (polarization) and spatial degrees of freedom. Experimental demonstrations spectacularly characterize the topological nature and the immanent rotational features of the light-field singularities. The review is based on the results obtained by its authors with a special attention to relevant works of other researchers.
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