Recent progress in two-dimensional superconductors with atomic-scale thicknesses is reviewed mainly from the experimental point of view. The superconducting systems treated here involve a variety of materials and forms: elemental-metal ultrathin films and atomic layers on semiconductor surfaces; interfaces and superlattices of heterostructures made of cuprates, perovskite oxides, and rare-earth metal heavy-fermion compounds; interfaces of electric-double-layer transistors; graphene and atomic sheets of transition-metal dichalcogenide; iron selenide and organic conductors on oxide and metal surfaces, respectively. Unique phenomena arising from the ultimate two-dimensionality of the system and the physics behind them are discussed.