Cobalt telluride has been identified as an efficient multifunctional electrocatalyst for oxygen and hydrogen evolution reactions and oxygen reduction reaction in alkaline medium. Both hydrothermally synthesized and electrodeposited, CoTe and CoTe2 show efficient electrocatalytic activities. CoTe shows better efficiency for OER with a low Tafel slope (43.8 mV dec-1) and lower overpotential (200 mV) at 10 mA cm-2 compared to CoTe2. DFT studies have also been performed which revealed that CoTe showed higher adsorption energy for intermediate-OH adsorption on the catalyst surface, which corresponds to the catalyst activation step. Comparison of the-OH adsorption energies (Eads) on different catalyst surfaces with the observed overpotential also revealed that this Eads can be used as an appropriate descriptor for benchmarking catalytic efficiencies. Both CoTe and CoTe2 exhibited improved OER catalytic efficiency compared to Co3O4, confirming the primary hypothesis that decreasing anion electronegativity enhances catalytic efficiency by virtue of increasing lattice covalency around the catalytically active site. The difference in OER catalytic activity between CoTe and CoTe2 could be explained from fundamental materials chemistry concepts by comparing their lattice structures which showed different packing density of catalytically active Co sites as well as varying unsaturation of Co-Terminated surfaces. Band structure calculations also corroborated such differences and could potentially explain the difference in activity due to observed differences in electron density distribution around the catalytically active Co site. The cobalt telluride compositions also showed moderate HER and ORR activity in alkaline medium, making them trifunctional catalysts which can be used in practical devices. Both CoTe and CoTe2 showed extensive functional and compositional stability for OER, HER, and ORR, under continuous operation in alkaline medium for over 24 h with less than 5% degradation of current density. The excellent compositional stability of each catalyst was revealed by detailed electrochemical measurements and surface and bulk analytical characterizations, which confirmed that there was no catalyst leaching even with long-Term operation and no other impurity enrichment in the electrolyte.