Modern geodetic and seismologic observations describe the behavior of fault slip over a vast range of spatial and temporal scales. Slip at sub-seismogenic speeds is evident from top to bottom of lithospheric faults and plays an important role throughout the earthquake cycle. Where earthquakes and tremor accompany slow slip, they help illuminate the spatiotemporal evolution of fault slip. Geophysical subsurface imaging and geologic field studies provide information about suitable environments of slow slip. In particular, exhumed fault and shear zones from various depths reveal the importance of multiple deformation processes and fault-zone structures. Most geologic examples feature frictionally weak and velocity-strengthening materials, well-developed mineral fabrics, and abundant veining indicative of near-lithostatic fluid pressure. To produce transient slow slip events and tremor, in addition to the presence of high-pressure fluids a heterogeneous fault-zone structure, composition, and/or metamorphic assemblage may be needed. Laboratory and computational models suggest that velocity-weakening slip patches smaller than a critical dimension needed for earthquake nucleation will also fail in slow slip events. Changes in fluid pressure or slip rate can cause a fault to transition between stable and unstable fault slip behavior. Future interdisciplinary investigations of slow fault slip, directly integrating geophysical, geological and modeling investigations, will further improve our understanding of the dynamics of slow slip and aid in providing more accurate earthquake hazard characterizations. •Geodetic and seismologic observations show that fault creep and slow slip events can occur at all depths of crustal faults.•Better understanding of slow slip requires integration of geophysical, geological, experimental, and modeling analyses.•There are many successful recipes for making a fault slip slowly.•Changes in fluid pressure or slip rate can cause a fault to transition between stable and unstable fault slip behavior.