"Oceanic upper mantle dynamics" may be defined as the ensemble of dynamical processes which by virtue of their relatively short length scales (few tens to a few hundred km) are largely confined to the upper mantle. The central thrust of the OMD initiative is to provide new constraints on models of such processes by exploiting emerging possibilities of high-resolution/large-aperture array observations. The field of oceanic upper mantle dynamics is vast and diverse. Rather than attempt the hopeless task of surveying it all, I have decided to concentrate on three themes that encompass a substantial proportion of current work in the field and are likely to continue to do so in the future: 1. Plumes in the upper mantle. While we are all but certain that mantle plumes exist, our observational images of them are still extraordinarily poor due to the small (ca. 100 km) length scales involved. OMD-style array observations thus promise to yield enormously improved understanding of the geometries of plumes in the upper mantle and their interaction with the oceanic lithosphere. By reason of their accessibility, size, and spectacular surface manifestations, the Hawaii and Iceland plumes necessarily hold a preeminent place. Detailed 3D fluid dynamical models exist for both Hawaii (Ribe and Christensen 1994, JGR; Morgan et al. 1995, JGR; Moore et al. 1998, Science) and Iceland (Ribe et al. 1995, EPSL; Ito et al. 1996, 1999, EPSL). However, these models have not yet been tested against tomographic images derived from wide-aperture arrays, and the available seismic evidence suggests that they may be unrealistic in significant ways (e.g., tilting of the plume conduit: Li et al. 2000, Nature; Shen et al. 2002, EPSL.) While Hawaii and Iceland are important, other significant hotspots should not be forgotten. One important configuration to study is that of a hotspot near (but not on) a ridge, such as the Galapagos hotspot. Perhaps the crucial outstanding question concerning such hotspots is how they communicate with the ridge: many lines of evidence seem to suggest the existence of a sublithospheric "channel" (Morgan 1978, JGR) but dynamical models have not been able to predict these. Wide-aperture array data could help resolve the question decisively. Another important group of hotspots are those above the Pacific "superswell". Courtillot et al. (2002, EPSL, submitted) have recently suggested that these hotspots may originate at transition-zone depths on top of a hot but chemically distinct "dome" that has risen from the deep mantle. This hypothesis may be testable with wide-aperture array seismic data. 2. Seismic anisotropy. Seismic anisotropy is ubiquitous in the oceanic upper mantle, and provides unique information on the state of deformation as a function of position. The link between the two is deformation-induced "lattice preferred orientation" (LPO) of olivine crystals, which exhibit strong anisotropy in both P and S wave velocities. During the past 10 years or so, considerable progress has been made in modeling the relation between LPO and deformation path, taking into account the effects of both intracrystalline slip and dynamic recrystallization (Wenk and Tome 1999, JGR; Kaminski and Ribe 2001, EPSL.) As a result, it is now possible to calculate directly from mantle flow models the seismic anisotropy that would be expected to develop at each point. Such calculations suggest that the relation between LPO and the local flow can be quite complex, even in relatively simple flow fields (Kaminski and Ribe 2002, G-Cubed, in press; (Blackman and Kendall 2002, G-Cubed, in press.) To date, detailed geodynamical modeling of seismic anisotropy has focussed on ridges (Blackman et al. 1996, Geophys. J. Int.; Toomey et al. 2002, EPSL) and subduction zones/backarc regions (Fischer et al. 1998, PAGEOPH; Hall et al. 2000, JGR) for which relatively simple 2D or 2.5D flow models can be constructed. A promising direction for the future is modeling of more realistic, fully 3D flows. Preliminary calculations by Browaeys and Ribe (in preparation) for a 3D convection model of plume-lithosphere interaction beneath Hawaii suggest that the resulting anisotropic structure is too complex to be represented by traditional layered models for which simple inversion schemes exist. Direct forward modeling will therefore be an indispensable tool for interpreting future array observations of seismic anisotropy. 3. Plate boundary formation and convection. The theory of plate tectonics, for all its extraordinary success, has had the unintended effect of encouraging a conception of lithospheric plates as distinct from the underlying convective circulation. An exciting direction of current research attempts to correct this problem by showing how plates themselves can be generated by thermal convection in fluids with complex rheology. The key issue in here is the formation and dynamics of the boundaries (convergent, divergent, and strike-slip) between plates. It has long been known that neither temperature-dependent nor power-law viscosity is adequate for generating the sorts of narrow "platelike" boundaries seen on earth (e.g., Christensen and Harder 1991, Geophys. J. Int.) Recent work has focussed on the role of more exotic rheological features, both singly and in combination: pre-existing weak zones (Zhong and Gurnis 1995, Science), stick-slip self-lubrication (Bercovici 1995, JGR), plastic yielding with melt-induced viscosity reduction (Tackley 2000, G-Cubed), and viscoplasticity with a low-viscosity asthenosphere (Richards et al. 2001, G-Cubed.) While the surface motions predicted by these simulations are strikingly "platelike", none has yet been able to reproduce all the features of the earth's surface tectonics, including isolated strike-slip motion and boundary longevity. A particularly important "subquestion" in this domain is that of subduction initiation. Here again there is no consensus, although numerous models have been proposed: slip on a preexisting fault zone (Toth and Gurnis 1998, JGR), failure under tensile stress (Kemp and Stevenson 1996, Geophys. J. Int.), thermo-mechanical feedback of low-temperature plasticity (Branlund et al. 2001, EPSL), and sediment loading combined with hydrolitic weakening (Regenauer-Lieb et al. 2001, Science). While the above models are promising, most are based on ad hoc assumptions about rheology that are not yet well constrained. A sounder physical basis for many of the underlying ideas has been provided by the two-phase damage theory of Bercovici et al. (2001, JGR), but large-scale computations using it are still in the future. Another critical need is to find suitable regions on earth where OMD-type array data might provide much-needed observational constraints on the mechanisms involved in plate boundary formation.