Nonlinear optics has proved to be one of the fastest-growing areas in contemporary physics, thanks to the development of high-intensity laser systems to generate ultrashort, high-power laser pulses. The response of a material in linear optics is directly proportional to the optical field applied to it. In nonlinear optics, however, there are involved complicated interactions wherein the polarization of the medium is nonlinearly dependent on the incident light's electric field. This results in a variety of effects such as harmonic generation, self-focusing, multiphoton absorption, and optical Kerr effects. The tremendous advancement of laser technology, especially the establishment of chirped pulse amplification (CPA), has opened up the path to generating intensities of over 10¹⁸ W/cm² and has allowed access to unprecedented exploitation of light-matter interactions in extreme conditions. The high-intensity regimes have expanded the area of fundamental studies as well as applications of nonlinear optics. Applications include high-harmonic generation (HHG), laser plasma formation, laser particle acceleration, and the generation of attosecond pulses to study ultrafast spectroscopy. Current research has concentrated on the nonlinear interaction dynamics in diverse media such as gases, solids, and plasmas. Specifically, laser filamentation, multiphoton ionization, and relativistic optics studies have unveiled new physical effects crucial for applications from high-resolution imaging to materials processing and biomedical diagnostics. In addition, nonlinear optical processes are crucial for the emergence of quantum optics and photonic devices, which provide new prospects in optical communication and information processing. This article summarizes recent theoretical and experimental progress in laser-matter interactions at high intensities, emphasizing important mechanisms, experimental methods, and emerging applications. Prospects for future directions are also addressed, focusing on the power of nonlinear optics to play a key role in scientific and technological advances in ultrafast science, plasma physics, and nuclear fusion driven by lasers.