We present investigations of optical phenomena and applications using highlynonlinear materials and geometries. We fabricated chalcogenide nanowires with extremely high aspect ratios and core diameters as small as 500 nm and lengths up to 10 cm. We showed the viability of these nanowires for nonlinear optical devices through demonstrations of nonlinear light-matter interactions in two power regimes. However, the limited durability of chalcogenide nanowires limits their viability for practical optical devices. We next investigate microspheres fabricated from amorphous arsenic triselenide (As2Se3). We developed a novel method of fabrication, which was based on heating using platinum coils in normal lab conditions and produced high optical quality samples with diameters ranging from 50 [mu]m to 500 [mu]m. We then developed a new method of coupling to high refractive index resonators using silicon waveguides. We demonstrated loaded Q's of 2.3×106 with light centered at 1550 nm. Nevertheless, thermal instabilities limit the practicality of using these resonators for enhanced nonlinear optical interactions. We next developed a novel temporal-imaging system that can be easily synchronized to an external clock source for use in a time-lens based on four-wave mixing for optical processing applications. Spectrally broadening the output of a repetition-rate-agile picosecond time-lens source via self-phase modulation in Corning® Vascade LS+ fiber resulted in a system that has the bandwidth to support optical measurement and processing with sub-picosecond resolutions. As a proof of concept, we implemented our temporal-imaging system in two time-lens systems: a time-to-frequency converter and a temporal-magnification system. We also showed that the timing jitter limits the resolution of our temporal-imaging system to 270 fs. Lastly, we used this temporal-imaging system to create an ultra-high-bandwidth fullfield, amplitude and phase, arbitrary waveform characterization system based on a temporal-phase measurement using heterodyning. We showed single-shot full-field reconstruction with 2.2-ps resolution over a record length of 250 ps.