  In this review paper, we comprehensively summarize numerical applications of
double-null formalism for studying dynamics within the theory of gravity. By
using the double-null coordinates, we can investigate dynamical black holes and
gravitational phenomena within spherical symmetry, including gravitational
collapse, formation of horizons and singularities, as well as evaporations.
This formalism can be extended to generic situations, where we can change
dimensions, topologies, the gravity sector, as well as the matter sector. We
also discuss its possible implications for black hole physics and particle
astrophysics. This strong numerical tool will have lots of future applications
for various research areas including general relativity, string theory, and
various approaches to quantum gravity.
