In this talk, I will discuss the algebraic properties of DNA cyclic codes. Reversible and reversible complement DNA cyclic codes over rings of order 16, 64, and 256 will also be explained. I will draw main focus on study of DNA cyclic codes some special finite non chain rings like Z_4+vZ_4, v^2=v, Z_4+uZ_4, u^2=1, and  F_2[u, v]/(u^2-1, v^3-v, uv-vu). Finally, I will draw some attention on constructions of DNA cyclic codes over some other finite Frobenious rings of order 4^n, n is positive.