The topology, geometry and algebra of unknotting tunnels

This article gives a survey of various aspects of the study of unknotting tunnels. We explain (1) various examples of unknotting tunnels, (2) effect of unknotting tunnels on symmetry groups, (3) topological rigidity and stable equivalence of unknotting tunnels, (4) geometric properties of unknotting tunnels for hyperbolic knots, (5) relation between two generator discrete groups and tunnel number one knots, and (6) application of the quantum SU(2) invariants to the tunnel number problem.