An intense femtosecond laser pulse can have an electric field strength which approaches or even exceeds the strength of the electric field that holds valence electrons in a transparent material to their ionic cores. In this regime, the interaction between the laser pulse and the material becomes highly nonlinear. Laser energy can be nonlinearly absorbed by the material, leading to permanent damage, and the materials nonlinear response to the laser field can, in turn, induce radical changes in the laser pulse itself. The nature of these nonlinear interactions, the changes produced in the material and to the laser pulse, as well as several practical applications are explored in this thesis. We measure the laser intensity required to damage bulk transparent materials and uncover the dominant nonlinear ionization mechanism for different laser wavelengths and material band gaps. Using optical and electron microscopy, we examine the morphology of the material changes induced by tightly-focused femtosecond laser pulses in bulk transparent materials, and identify several mechanisms by which material changes are produced. We show that a high repetition rate train of femtosecond laser pulses can provide a point source of heat located inside the bulk of a transparent material, an effect which no other technique can achieve. The mechanism for white-light continuum generation is uncovered through measurement of the laser wavelength, the material band gap, and the external focusing angle dependence of the continuum spectrum. Using a time-resolved imaging technique, we follow the dynamics of the laser-produced plasma over eight orders of magnitude in time, revealing picosecond time scale dynamics that have not been previously observed. Finally, we discuss applications in direct writing of optical waveguides and in sub-cellular laser surgery.