The authors discuss affine regularity of polygons in the general setting of polygons in an affine plane over an arbitrary field. They present seven equivalent ways to define affine regularity, one of which appears for the first time; the other definitions had been known earlier [for example, see \textit{H. S. M. Coxeter}, Abh. Math. Semin. Univ. Hamburg 34, 38-58 (1969; Zbl 0187.42501)]. In the Euclidean plane, an \(n\)-gon is affinely regular if and only if it is the image of a regular \(n\)-gon under an affinity. However, this does not remain true in the general setting. The authors also describe an application of Chebyshev polynomials to obtain results about parameters associated with affinely regular polygons.