The viscosities of matters under extreme conditions, i.e. warm dense matter (WDM) and hot dense matter (HDM), have significant applications in various fields, such as the design of inertial confinement fusion targets, the astrophysical structure evolution, and the interfacial instability and mixing development under extreme conditions. Since the temperature and pressure ranges accessible by experimental techniques for viscosity measurement are very limited, the acquisition of viscosity data under extreme conditions mainly relies on theoretical calculations. This work introduces a variety of molecular dynamics (MD) methods and models for calculating the viscosities of WDM and HDM, they being quantum MD (QMD), orbital-free MD (OFMD), average atom model combined with hypernetted chain (AAHNC), effective potential theory combined with average atom model (EPT+AA), hybrid kinetics MD (KMD), integrated Yukawa viscosity model (IYVM), Stanton-Murillo transport model (SMT), pseudo-ion in jellium (PIJ), one-component plasma model (OCP), and random-walk shielding-potential viscosity model (RWSP-VM). Simultaneously, the viscosities of various elements obtained by these methods are shown, ranging from low to high atomic number (Z), i.e., H, C, Al, Fe, Ge, W, and U. The accuracy and the applicability of each method are analyzed in detail by comparison. RWSP-VM, which is based on physical modeling and independent of MD data, has comparable accuracy to simulation data over a wide range of temperature and pressure, and is an efficient method of obtaining viscosity data of WDM and HDM. This work will pave the way for calculating the shear viscosities under extreme conditions, and may play an important role in promoting the relevant applications. The data calculated from RWSP-VM in this work are openly available at https://doi.org/10.57760/sciencedb.j00213.00180.
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