Duality means that two apparently different theories describe the same physics, often in complementary regimes. Examples include electric-magnetic duality, weak-strong coupling dualities, and gauge/gravity duality. Duality is one of the most powerful ideas in modern theoretical physics because it can relate hard problems to tractable ones.

Lattice field theory, instanton calculus, bootstrap methods, large-$N$ expansions, semiclassical analysis, and numerical simulations all address regimes inaccessible to straightforward perturbation theory. These techniques are essential for understanding confinement, strongly coupled matter, and critical phenomena.

The combination of symmetry, topology, renormalization, and duality often gives the deepest insight into a theory. Rather than asking for the exact microscopic equations first, theorists frequently ask what must be true at low energies, under coarse-graining, or across different phases.

Open problems include the microscopic origin of black hole entropy, the nature of quantum spacetime, the confinement mechanism in non-Abelian gauge theory, the hierarchy problem, the cosmological constant problem, and the emergence of classical behavior from quantum theory. Progress often comes from combining methods across subfields rather than from a single formal breakthrough.