Seismic swarms are often interpreted to be driven by natural fluid pressurization in the Earth’s crust, when seismicity is observed to spread away from a common origin and follows approximately a square-root-of-time pattern of growth. On the other hand, a growing body of literature suggests that aseismic fault slip seems to be a frequent result of fluid injections and may trigger seismicity due to the stress transfer of quasi-statically propagating ruptures in critically stressed regions. Although in some conditions a nominal pore pressure perturbation front may evolve proportionally to the square root of time, much less is known about the temporal patterns of fluid-driven aseismic slip fronts. The latter hinders efforts to distinguish whether some seismic swarms are driven by aseismic slip episodes or not. In this contribution, we provide an extensive set of physics-based solutions that describes the evolution of fluid-driven aseismic slip fronts for a wide range of conditions in terms of in-situ stress state and fluid flow. Our solutions show that fluid-driven aseismic slip fronts may result in many different patterns of propagation, depending on the characteristics of the fluid source (e.g., constant-pressure source, constant-rate source, among others) and also if simplified 2-D or fully 3-D elasticity is considered. Other parameters such as the initial stress state and fault hydraulic properties are also relevant in the propagation of the slip fronts. Our family of solutions includes cases in which aseismic slip fronts propagate following a square-root-of-time dependence, a linear expansion with time, power laws of time with exponents lower than ½, and some other more complex evolutions. These results are based on the model of a fluid-driven frictional shear crack that propagates on a planar fault interface characterized by a constant friction coefficient and a constant permeability, embedded in an infinite linearly elastic medium with an initially uniform state of stress. Although the basic assumptions of the model are simple, it results in a significant amount of complexity in terms of possible spatio-temporal patterns of rupture propagation. Since a constant friction coefficient corresponds to a fault interface with zero fracture energy, we show by analyzing the rupture-front energy balance of fluid-driven aseismic slip transients with non-zero fracture energy, that an asymptotic regime in which the fracture energy is negligible is always ultimately reached. This regime is approached asymptotically when the rupture has propagated over a distance larger than a characteristic length-scale depending on the frictional fracture energy and the in-situ stress state. We expect our results to provide a simple means to interpret observations of seismic swarms for which fluid-driven aseismic slip transients are thought to be a relevant mechanism in the triggering of seismicity.