This talk is concerned with the numerical solutions to the flow and transport problems in fractured porous media. A dimensionally reduced fracture model written in mixed form is considered, where the fracture is assumed to have larger permeability than the surrounding area and is modeled as an interface between subdomains. We aim to develop fast-convergent and accurate global-in-time domain decomposition (DD) methods for such reduced models. We first focus on the flow problem of a single phase, compressible fluid and derive its reduced fracture models. New global-in-time DD methods together with the existing methods for such models are then discussed. Numerical experiments with different types of fracture are presented to verify and compare the performance of the proposed methods with different time steps in the fracture and in the rock matrix. These methods are then extended to the case of linear advection-diffusion equations where global-in-time domain decomposition is coupled with operator splitting to treat the advection and the diffusion separately by different numerical schemes and with different time steps.