The special position of the Riccati differential equation are not all entire, actually admits meromorphic solutions in the complex plane. This article is mainly devoted to presenting some contributions to this problem.We should perhaps point out here that the problem of whether such meromorphic solutions are rational or transcendental in the case when the coefficients are rational, has been treated earlier by H. Wittich [13] and [17].In this article, the term "meromorphic function" means meromorphic in the wholo complex plane, unless otherwise explicitly stated. Almost all of our treatment is concentrated in the special case of (1.1):