A survey on smooth unknotting of a surface-knot in the 4-space

It is explained how a smooth surface-knot in 4-space with infinite cyclic fundamental group is a trivial surface-knot (i.e., the boundary of a smoothly embedded handlebody) in the 4-space. It is also explained how a smooth surface-link in 4-space with meridian-based free fundamental group is a trivial surface-link (i.e., the boundary of smoothly embedded disjoint handlebodies) in the 4-space. For these proofs, the concept of an orthogonal 2-handle pair on a surface-link is introduced and the properties are explained, with the property of uniqueness being particularly essential.