  Tensor network methods are a class of numerical tools and algorithms to study
many-body quantum systems in and out of equilibrium, based on tailored
variational wave functions. They have found significant applications in
simulating lattice gauge theories approaching relevant problems in high-energy
physics. Compared to Monte Carlo methods, they do not suffer from the sign
problem, allowing them to explore challenging regimes such as finite chemical
potentials and real-time dynamics. Further development is required to tackle
fundamental challenges, such as accessing continuum limits or computations of
large-scale quantum chromodynamics. In this work, we review the
state-of-the-art of Tensor Network methods and discuss a possible roadmap for
algorithmic development and strategies to enhance their capabilities and extend
their applicability to open high-energy problems. We provide tailored estimates
of the theoretical and computational resource scaling for attacking large-scale
lattice gauge theories.
