  The pressure tensor (equivalent to the negative stress tensor) at both
microscopic and macroscopic levels is fundamental to many aspects of
engineering and science, including fluid dynamics, solid mechanics, biophysics,
and thermodynamics. In this perspective paper, we review methods to calculate
the microscopic pressure tensor. Connections between different pressure forms
for equilibrium and non-equilibrium systems are established. We also point out
several challenges in the field, including the historical controversies over
the definition of the microscopic pressure tensor; the difficulties with
many-body and long-range potentials; the insufficiency of software and
computational tools; and the lack of experimental routes to probe the pressure
tensor at the nanoscale. Possible future directions are suggested.
