Optical microscopy is one of the oldest and most important imaging techniques; however, its far-field resolution is diffraction-limited. In this dissertation, we proposed and developed a novel method of optical microscopy with super-resolution by using high-index dielectric microspheres immersed in liquid and placed on the surface of the structures under study. We used barium titanate glass microspheres with diameters of D∼2-220 μm and refractive indices n∼1.9-2.1 to discern minimal feature sizes ∼λ/4 (down to ∼λ/7) of various photonic and plasmonic nanostructures, where λ is the illumination wavelength. We studied the magnification, field of view, and resolving power, in detail, as a function of sphere sizes.We studied optical coupling, transport, focusing, and polarization properties of linear arrays of dielectric spheres. We showed that in arrays of spheres with refractive index n=√3, a special type of rays with transverse magnetic (TM) polarization incident on the spheres under the Brewster's angle form periodically focused modes with radial polarization and 2D period, where D is the diameter of the spheres. We showed that the formation of periodically focused modes in arrays of dielectric spheres gives a physical explanation for beam focusing and extraordinarily small attenuation of light in such chains. We showed that the light propagation in such arrays is strongly polarization-dependent, indicating that such arrays can be used as filters of beams with radial polarization. The effect of forming progressively smaller focused beams was experimentally observed in chains of sapphire spheres in agreement with the theory.We expanded the concept of periodically focused modes to design a practical device for ultra-precise contact-mode laser tissue-surgery, with self-limiting ablation depth for potential application in retina surgery. By integrating arrays of dielectric spheres with infrared hollow waveguides and fibers, we fabricated prototypes of the designs and tested them with an Er:YAG laser. Furthermore, we proposed another design based on conical arrays of dielectric spheres to increase the coupling efficiency of the probe.