The cone penetration test is an effective, rapid, and minimally invasive method used for the finescale characterization of the mechanical and transport properties of soils. Despite many decades of use, a coherent methodology for the inclusion of tip-local effects of partial-drainage in the reduction of penetrometer data remains elusive. This shortfall is partially addressed through the use of models capable of representing both the rate of advance of the penetrometer, and the morphology and related soil and fluid flow-fields which develop around the tip and along the shaft. These studies are informed by models of varying complexity, representing components of the full spectrum of response - undrained through drained. These include models representing migrating volume dislocations of infinitesimal size, replicating blunt and tapered penetrometers, spherical static models representing pseudo-steady-state flow and failure, and Lagrangian models incorporating convective flow and failure. Of these, the latter yields the most comprehensive view of response, accommodating the failuremediated pore-pressure field which develops around the penetrometer tip, and its concurrent advection and dissipation in the soil flow-field which naturally evolves. The utility of these models is discussed in defining the form of rate effects in penetration, and in their use for the interpretation of uCPT data for transport and mechanical properties.