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[Display omitted] By combining experiments and modeling from three US national laboratories, we explore compressive strength in a well-characterized material, tantalum, across pressures from zero to over 350 GPa, strain-rates from 10 − 3 /s to 10 8 /s and temperatures from 148 K to 3800 K. Strength values from 40+ experiments are shown to vary by nearly two orders of magnitude, from 0.15 GPa to over 10 GPa. Cross-comparison of these results allows pressure and strain-rate dependencies to be isolated, and strength increases more significantly with pressure than with strain rate over the range studied. Simulations using Preston-Tonks-Wallace, Livermore Multi-Scale, and Kink-Pair strength models test modeling capabilities and provide further insight into strength mechanics. The widely-used assumption in those models of shear-modulus scaling underpredicts strength by a factor of about two at extreme pressures in pulsed-power planar ramp-release experiments, which largely isolate pressure effects. Richtmyer-Meshkov Instability experiments, which largely isolate strain rate effects at ∼ 10 7 /s, suggest that modeling assumptions about mechanisms at the highest rates need further study. Laser-driven Rayleigh-Taylor instability experiments, which simultaneously probe extreme pressures and strain rates, provide both model and cross-platform experimental validation. The large-scale collaborative nature of this study covers a wide span of experimental conditions and modeling approaches, allowing for extraordinary insight into dynamic strength. [ABSTRACT FROM AUTHOR]