Describes known results about Steiner systems — (v,k,t)-covering designs in which every t-set is covered exactly once — listing the known infinite families for t = 2 and 3 (Steiner triple and quadruple systems, affine/spherical/projective geometries, unitals, Denniston designs) and the 13 known Steiner 5-designs from S(5,6,12) to S(5,6,244). Explicit systems with small parameters are reachable through the La Jolla Covering Repository.