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In this article we survey some recent progress in research on codes over the finite ring B_(2,q). The ring B_(2,q) has special connections with the finite field F_q such that many properties of linear codes over B_(2,q) can be derived from classical linear codes over F_q. We focus on cyclic codes over B_(2,q) and their generalizations such as skew cyclic codes and skew cyclic codes with derivation over B_(2,q). We also observe the concept of double cyclic codes over B_(2,q) and their generalizations.

codes over finite rings; cyclic codes; double cyclic codes; skew cyclic codes; skew cyclic codes with derivation