Material equation-of-state (EOS) models, generally providing the pressure and internal energy for a given density and temperature, are required to close the equations of hydrodynamics. As a result they are an essential piece of physics used to simulate inertial confinement fusion (ICF) implosions. Historically, EOS models based on different physical/chemical pictures of matter have been developed for ICF relevant materials such as the deuterium (D2) or deuterium-tritium (DT) fuel, as well as candidate ablator materials such as polystyrene (CH), glow-discharge polymer (GDP), beryllium (Be), carbon (C), and boron carbide (B4C). The accuracy of these EOS models can directly affect the reliability of ICF target design and understanding, as shock timing and material compressibility are essentially determined by what EOS models are used in ICF simulations. Systematic comparisons of current EOS models, benchmarking with experiments, not only help us to understand what the model differences are and why they occur, but also to identify the state-of-the-art EOS models for ICF target designers to use. For this purpose, the first Equation-of-State Workshop, supported by the US Department of Energy’s ICF program, was held at the Laboratory for Laser Energetics (LLE), University of Rochester on 31 May–2nd June, 2017. This paper presents a detailed review on the findings from this workshop: (1) 5–10% model-model variations exist throughout the relevant parameter space, and can be much larger in regions where ionization and dissociation are occurring, (2) the D2 EOS is particularly uncertain, with no single model able to match the available experimental data, and this drives similar uncertainties in the CH EOS, and (3) new experimental capabilities such as Hugoniot measurements around 100 Mbar and high-quality temperature measurements are essential to reducing EOS uncertainty.