Fracture of polymer gels is often time- and rate-dependent. Subject to a constant load, a gel specimen may fracture immediately or after a delay (time-dependent, delayed fracture). When a crack grows in a gel, the fracture energy may depend on the crack speed (rate-dependent). The underlying mechanisms for the time- and rate-dependent fracture of gels could include local molecular processes, polymer viscoelasticity, and solvent diffusion coupled with deformation (poroelasticity). This paper focuses on the effects of poroelasticity. A path-independent, modified J-integral approach is adopted to define the crack-tip energy release rate as the energetic driving force for crack growth in gels, taking into account the energy dissipation by solvent diffusion. For a stationary crack, the energy release rate is time-dependent, with which delayed fracture can be predicted based on a Griffith-like fracture criterion. For steady-state crack growth in a long-strip specimen, the energy release rate is a function of the crack speed, with rate-dependent poroelastic toughening. With a poroelastic cohesive zone model, solvent diffusion within the cohesive zone leads to significantly enhanced poroelastic toughening as the crack speed increases, rendering a rate-dependent traction-separation relation. While most of the results are based on a linear poroelastic formulation, future studies may extend to nonlinear theories with large deformation. In addition to the poroelastic effects, other mechanisms such as viscoelasticity and local fracture processes should be studied to further understand the time and rate-dependent fracture of polymer gels.