Abstract Fractures are common features in many well-known reservoirs. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones and are connected to numerous fractures that have varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (rather than connected network dual-porosity systems). In this paper we investigate the pressure transient behavior of continuously and discretely naturally fractured reservoirs using semi-analytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite- and/or infinite-conductivity fractures with different lengths and orientations. In some of our earlier papers, we showed that in terms of pressure transient, neither continuously nor discretely fractured reservoirs behave like the Warren and Root (1963) dual-porosity model. Unlike the single-derivative shape of the Warren and Root model, derivatives of pressure transient tests in fractured reservoirs exhibit more than 10 flow regimes. There are seven important factors that dominate the pressure transient test-flow regime behavior of fractured and faulted reservoirs; i.e., fractures and/or faults that: 1) intersect the wellbore parallel to its axis, with a dipping angle of 90° (vertical fractures), including hydraulic fractures; 2) intersect the wellbore with dipping angles from 0° to less than 90°; 3) are in the vicinity of the wellbore; 4) have extremely high- or low-fracture and fault conductivities; 5) have various sizes and distributions; 6) have high- and low-matrix block permeabilities; and 7) have damaged fractures (skin zone) due to drilling and completion operations and fluids. All flow regimes associated with these factors are shown for a number of continuously and discretely fractured reservoirs with different well and fracture configurations. For a few cases, these flow regimes are compared with those from the field data. History matchings of the pressure transient data generated by using our discretely and continuously fractured reservoir model with the Warren and Root (1963) type dual-porosity models are also presented.