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Deep-seated slow slip and tremor (SST), including slow slip events, episodic tremor and slip, and low-frequency earthquakes, occur downdip of the seismogenic zone of numerous subduction megathrusts and plate boundary strike-slip faults. These events represent a fascinating and perplexing mode of fault failure that has greatly broadened our view of earthquake dynamics. In this contribution, we review constraints on SST deformation processes from both geophysical observations of active subduction zones and geological observations of exhumed field analogues. We first provide an overview of what has been learned about the environment, kinematics and dynamics of SST from geodetic and seismologic data. We then describe the materials, deformation mechanisms, and metamorphic and fluid pressure conditions that characterize exhumed rocks from SST source depths. Both the geophysical and geological records strongly suggest the importance of a fluid-rich and high fluid pressure habitat for the SST source region. Additionally, transient deformation features preserved in the rock record, involving combined frictional-viscous shear in regions of mixed lithology and near-lithostatic fluid pressures, may scale with the tremor component of SST. While several open questions remain, it is clear that improved constraints on the materials, environment, structure, and conditions of the plate interface from geophysical imaging and geologic observations will enhance model representations of the boundary conditions and geometry of the SST deformation process. This article is part of a discussion meeting issue ‘Understanding earthquakes using the geological record’., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379 (2193), ISSN:1364-503X, ISSN:1471-2962