A Steiner triple system (V, B) is a combinatorial design consisting of a set V of v points and a set B of three-element blocks, with the condition that each pair from V appears in exactly one block from B. Steiner triple systems STS(v) exist if and only if v ≡ 1, 3 (mod 6). In this paper, the properties and existence conditions of Steiner triple systems are described, methods of their construction are presented, and an overview is given of the challenging problem of determining isomorphism and classification of Steiner triple systems. Latin squares, as well as symmetric idempotent quasigroups and symmetric half-idempotent quasigroups, are described. These structures are necessary for Bose’s construction and the modified Skolem construction of Steiner triple systems. Bose’s construction uses an idempotent quasigroup, while Skolem’s construction uses a half-idempotent quasigroup. The concept of isomorphism of Steiner triple systems is explored. The open problem of enumeration and classification of Steiner triple systems is described. A practical application of Steiner triple systems in experiment design and planning is presented, and an implemented web-application that uses Steiner triple systems for efficient experimental planning is described.