  This is a survey on the theory of skew-cyclic codes based on skew-polynomial
rings of automorphism type. Skew-polynomial rings have been introduced and
discussed by Ore (1933). Evaluation of skew polynomials and sets of (right)
roots were first considered by Lam (1986) and studied in great detail by Lam
and Leroy thereafter. After a detailed presentation of the most relevant
properties of skew polynomials, we survey the algebraic theory of skew-cyclic
codes as introduced by Boucher and Ulmer (2007) and studied by many authors
thereafter. A crucial role will be played by skew-circulant matrices. Finally,
skew-cyclic codes with designed minimum distance are discussed, and we report
on two different kinds of skew-BCH codes, which were designed in 2014 and
later.
