The main idea of this review is to trace the interrelations and inter-transitions between the basic concepts and approaches of the correlation optics (including the light coherence) and the singular optics dealing with networks of “exceptional” points of light fields. The principles and examples are described of formation of light fields with required structures (amplitude, phase and polarization distributions, spectral properties as well as the internal energy flows and energy gradients responsible for optical forces) via superpositions of model optical fields of simple standard configurations and under controllable correlation conditions. The theoretical and experimental results, obtained by the authors and other researchers, demonstrate possibilities of the general approach to the complex fields formation with spatial and polarization inhomogeneities. A special topic, considered in more detail, is the interaction of structured optical fields with the media containing suspended micro- and nanoparticles, their inhomogeneous heating by the laser radiation and the accompanying self-diffraction and self-focusing phenomena. Possible light-induced phase transitions and controllable generation of the gas-vapor microbubbles in the medium are discussed. Specific optical singularities in polychromatic light fields are analyzed in connection to the field coherence. Some experimental solutions for revealing the fine structure of optical fields by means of the interference schemes are presented. Practical applications for the micromanipulation techniques, optical diagnostics of remote and random objects, optical treatment and laboratory practice in biology and medicine are described and discussed.