This dissertation focuses mainly on three topics: (1) mixed-mode branching and segmentation of hydraulic fractures in brittle materials, (2) hydraulic fracture propagation in particulate materials, and (3) hydraulic fracturing in water flooding conditions. Mixed-mode loading is one of the primary causes of fracture branching and segmentation in brittle materials. We conducted the first laboratory experiments on the mixed mode I+III hydraulic fracturing. We found that a KIII/KI ratio as small as ~1% is sufficient for fracture front segmentation. In reality, such a small mode III component is always expected, for example, due to the small deviations of the fracture shape from planar. Thus, we concluded that fracture segmentation is likely to accompany growth of most, if not all, real hydraulic fractures. We also proposed a theoretical model that captures the main features of experimental observations and indicates the importance of the hydraulic effect of segmentation. Particulate materials often exhibit pronounced non-linear behavior and yielding even at relatively small loads. In order to adequately describe hydraulic fracturing in particulate materials with low or no cohesion, plasticity at the crack tip must be explicitly considered. We investigated the shear band mechanism of strain localization at the fracture front. This mechanism takes into account the fact that cohesionless material can not bear tension, and is in compression everywhere, including near the fracture front. To verify the shear band hypothesis, we conducted numerical simulations of the plastic deformation at the tip of a fracture in particulate material with strain softening. Our model describes the shear bands by properly placed and oriented dislocations. The model results are consistent with experimental observations. Water flooding, which in certain important cases, can result in processes resembly hydraulic fracturing by a low-viscosity fluid with extremely high leak-off. It is difficult to simulate this process in the laboratory. To investigate the fracture initiation mechanism in water flooding conditions, we conducted a numerical simulation of fluid injection into particulate material by using the discrete element code PFC2D. We also considered an analytical model of cavity initiation based on the fluidization mechanism. The estimates given by this model fit remarkably well with the numerical simulation results.