This thesis presents the theoretical and experimental investigation of volume holography operated with broadband/polychromatic light sources, i.e., in both continuous-wave (linear) and femtosecond-pulse (nonlinear) regimes. The first chapter reviews the concept of volume holography and provides a tacit introduction to some basic properties of volume holograms and compares the operation of holograms in the spatial and temporal domains, preparing the readers for later chapters. The second chapter introduces a powerful theoretical tool for the analysis of volume holograms in the reflection geometry: the matrix formulation, laying the foundation for the application of holographic gratings utilized as WDM filters. The third chapter takes into consideration the effects of the practically inevitable finite beam-widths. By means of Fourier decomposition, the deviation of the filtering properties of volume holographic gratings from the ideal plane-wave case can be satisfactorily explained and predicted. Experiments and simulations are performed and compared to confirm the validity of the theory. Volume holographic gratings in the reflection geometry serve as excellent WDM filters for telecommunication purposes thanks to their low cross-talk and readily engineered filtering properties. The theoretical design and experimental realization of athermal holographic filters are presented in the fourth chapter. By incorporating a passive, thermally actuated MEMS mirror, the temperature dependence of the Bragg wavelength of a holographic filter can be compensated. The analysis of holographic gratings in the 90 degree geometry requires a two dimensional theory. The relevant boundary conditions give rise to some peculiar behaviors in this configuration. Theory, simulations and some experimental results of the 90-degree holography are presented in chapter five. The sixth chapter delves into the subject of instantaneous Kerr index grating established by two intense, interfering femtosecond (pump) pulses at 388 nm owing to the omnipresent third-order nonlinearity. The coupled-mode equations describing the incident and diffracted (probe) pulses at 776 nm are written down; the solution is experimentally corroborated. It is further demonstrated that the temporal resolution in such a holographic pump-probe configuration does not degrade appreciably as the angular separation between pump pulses increases. Chapter seven investigates the nonlinear absorption processes in lithium niobate crystals with femtosecond pulses. The model of two-photon absorption well explains and anticipates the transmission coefficients of single pulses over a wide range of intensity. Collinear pump-probe transmission experiments are then carried out to look into the nonlinear absorption suffered by the probe pulse at 776 nm owing to the pump pulse at 388 nm; the dependence of the probe pulse transmission coefficient on the time delay between pump and probe pulses is characterized by a dip and a long-lasting plateau, which are attributed, respectively, to direct two-photon transitions involving pump and probe photons and the existence of free carriers. Building on the experimental experience and theoretical understanding of the previous two chapters, the results of holographic pump-probe experiments in lithium niobate crystals are presented in the final chapter. The behavior is much more complicated because it encompasses all phenomena explored in the two preceding chapters, i.e., both the real and imaginary parts of the third-order susceptibility come into play in the instantaneous material response; furthermore, another mixed grating due to excited charge carriers exists long after the pump pulses pass through. Valuable information on the grating formation process is obtained thanks to the sub-picosecond temporal resolution of such configurations.