Thermogalvanic cells exploit the entropy changes inherent in redox reactions to couple a flow of ions to a flow of heat. While these systems have been studied in the past in the context of thermal energy harvesting, few chemistries have been identified with the requisite low activation energies, high entropy changes, and high overall reversibility for effectively coupling thermal and electrical energy flows. However, recent developments in the redox flow battery community have opened up many avenues for improvement in thermogalvanics, especially in the nearly-unstudied but complementary field of electrochemical refrigeration, which offers a potentially environmentally and climate-friendly means of climate control. In this presentation, we develop the thermogalvanic concept from basic principles, derive the fundamental relationship between cold-side activation energy and overall entropy change required to yield a cooling effect, provide an accounting of the dominant loss mechanisms encountered in these systems, and review a number of proposed chemistries and system configurations, including charge-cycling, static electrolyte, and flow systems with and without membrane separators. We present a matrix of candidate redox couples and describe the criteria for their utilization in thermogalvanic systems, as well as favorable operating regimes for each in terms of temperature, partial pressure of gaseous reactants, electrolyte composition, and catalyst and support materials. Finally, we present a novel 4-electrode vanadium-bromide flow cell for electrochemical refrigeration. The 4-electrode cell is projected to produce a cooling power up to 20mW/cm^2 of device area with a cooling COP of 0.9, based on a model accounting for activation losses (based on Butler-Volmer kinetics and measured exchange current and transfer coefficient values), concentration polarization, and thermal losses. This model is described in full, and power curves are derived for varying temperature, pressure, pump power, and electrolyte concentration and composition. Additionally, we present the results from preliminary electrochemical and thermal testing in a 2-electrode static-electrolyte cell. The preliminary test cell consists of two identical carbon paper electrodes separated with a 50um polyethylene mesh, and built into a carbon-aerogel insulated glass calorimeter, with a total interior volume barely exceeding that of the porous electrodes and separator so as to minimize the heat capacity of the cell. The cell also includes a porous frit connection to a reference electrode. This system is characterized via potentiostatic and galvanostatic techniques, and its transport characteristics are established via impedance spectroscopy. Finally, measured cooling power is compared to a model of the 2-electrode cell, and used to validate the model of the full 4-electrode flow-cell electrochemical refrigerator.